Journal articles on the topic 'Maximal nonprincipal right ideal'
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1
Johnson, C. A. "Distributive ideals and partition relations." Journal of Symbolic Logic 51, no. 3 (September 1986): 617–25. http://dx.doi.org/10.2307/2274018.
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It is a theorem of Rowbottom [12] that ifκis measurable andIis a normal prime ideal onκ, then for eachλ<κ,In this paper a natural structural property of ideals, distributivity, is considered and shown to be related to this and other ideal theoretic partition relations.The set theoretical terminology is standard (see [7]) and background results on the theory of ideals may be found in [5] and [8]. Throughoutκwill denote an uncountable regular cardinal, andIa proper, nonprincipal,κ-complete ideal onκ.NSκis the ideal of nonstationary subsets ofκ, andIκ= {X⊆κ∣∣X∣<κ}. IfA∈I+(=P(κ) −I), then anI-partitionofAis a maximal collectionW⊆,P(A) ∩I+so thatX∩ Y ∈IwheneverX, Y∈W, X≠Y. TheI-partitionWis said to be disjoint if distinct members ofWare disjoint, and in this case, fordenotes the unique member ofWcontainingξ. A sequence 〈Wα∣α<η} ofI-partitions ofAis said to be decreasing if wheneverα<β<ηandX∈Wβthere is aY∈Wαsuch thatX⊆Y. (i.e.,WβrefinesWα).
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Birkenmeier, Gary F., Dinh Van Huynh, Jin Yong Kim, and Jae Keol Park. "Extending the Property of a Maximal Right Ideal." Algebra Colloquium 13, no. 01 (March 2006): 163–72. http://dx.doi.org/10.1142/s1005386706000174.
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We extend various properties from a direct summand X of a module M, whose complement is semisimple, to its trace in M or to M itself. The case when MR = RR and the properties are injectivity or P-injectivity is fully described. As applications, we extend some known results for right HI-rings and give a new characterization of semisimple rings. We conclude this paper by giving some conditions that yield the self-injectivity of von Neumann regular rings.
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Shatila, Maya A. "On Some Properties of *-annihilators and *-maximal Ideals in Rings with Involution." Journal of Mathematics Research 8, no. 1 (January 6, 2016): 1. http://dx.doi.org/10.5539/jmr.v8n1p1.
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We describe the ∗-right annihilator (∗-left anihilator) of a subset of a ring and we investigate the relationships between the right annihilator and ∗-right annihilator. These connections permit the transfer of various properties from annihilators to ∗-annihilators . It is known that the quotient ring constructed from a ring and a maximal ideal is a field, whereas we prove that the quotient ring constructed from a ring and a *-maximal ideal is not a *-field. Equivalent definitions to ∗-regular ring are given.
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Zhang, Yong. "Maximal ideals and the structure of contractible and amenable Banach algebras." Bulletin of the Australian Mathematical Society 62, no. 2 (October 2000): 221–26. http://dx.doi.org/10.1017/s0004972700018694.
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Properties of minimal idempotents in contractible and reflexive amenable Banach algebras are exploited to prove that such a kind of Banach algebra is finite demensional if each maximal ideal is contained in a maximal left or a maximal right ideal that is complemented as a Banach subspace. This result covers several known results on this subject.
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Sun, Shu-Hao. "Rings in which every prime ideal is contained in a unique maximal right ideal." Journal of Pure and Applied Algebra 78, no. 2 (April 1992): 183–94. http://dx.doi.org/10.1016/0022-4049(92)90096-x.
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ANDRUSZKIEWICZ, R. R. "ON MAXIMAL ESSENTIAL EXTENSIONS OF RINGS." Bulletin of the Australian Mathematical Society 83, no. 2 (October 29, 2010): 329–37. http://dx.doi.org/10.1017/s0004972710001759.
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AbstractThe main purpose of this paper is to give a new, elementary proof of Flanigan’s theorem, which says that a given ring A has a maximal essential extension ME(A) if and only if the two-sided annihilator of A is zero. Moreover, we discuss the problem of description of ME(A) for a given right ideal A of a ring with an identity.
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Nicholson, W. K. "On a Theorem of Burgess and Stephenson." Canadian Mathematical Bulletin 62, no. 3 (December 6, 2018): 603–5. http://dx.doi.org/10.4153/s0008439518000619.
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AbstractA theorem of Burgess and Stephenson asserts that in an exchange ring with central idempotents, every maximal left ideal is also a right ideal. The proof uses sheaf-theoretic techniques. In this paper, we give a short elementary proof of this important theorem.
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REYES, MANUEL L. "A ONE-SIDED PRIME IDEAL PRINCIPLE FOR NONCOMMUTATIVE RINGS." Journal of Algebra and Its Applications 09, no. 06 (December 2010): 877–919. http://dx.doi.org/10.1142/s0219498810004294.
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Completely prime right ideals are introduced as a one-sided generalization of the concept of a prime ideal in a commutative ring. Some of their basic properties are investigated, pointing out both similarities and differences between these right ideals and their commutative counterparts. We prove the Completely Prime Ideal Principle, a theorem stating that right ideals that are maximal in a specific sense must be completely prime. We offer a number of applications of the Completely Prime Ideal Principle arising from many diverse concepts in rings and modules. These applications show how completely prime right ideals control the one-sided structure of a ring, and they recover earlier theorems stating that certain noncommutative rings are domains (namely, proper right PCI rings and rings with the right restricted minimum condition that are not right artinian). In order to provide a deeper understanding of the set of completely prime right ideals in a general ring, we study the special subset of comonoform right ideals.
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Mohamed, Saad, and Bruno J. Müller. "Structure of pseudo-semisimple rings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 50, no. 1 (February 1991): 53–66. http://dx.doi.org/10.1017/s1446788700032547.
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AbstractA ring R is called right pseudo-semisimple if every right ideal not isomorphic to R is semisimpie. Rings of this type in which the right socle S splits off additively were characterized; such a ring has S2 = 0. The existence of right pseudo-semisimple rings with zero right singular ideal Z remained open, except for the trivial examples of semisimple rings and principal right ideal domains. In this work we give a complete characterization of right pseudo-semisimple rings with S2 = 0. We also give examples of non-trivial right pseudo-semisimple rings with Z = 0; in fact it is shown that such rings exist as subrings in every infinite-dimensional full linear ring. A structure theorem for non-singular right pseudo-semisimple rings, with homogeneous maximal socle, is given. The general case is still open.
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Brungs, H. H. "Bezout Domains and Rings with a Distributive Lattice of Right Ideals." Canadian Journal of Mathematics 38, no. 2 (April 1, 1986): 286–303. http://dx.doi.org/10.4153/cjm-1986-014-2.
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It is the purpose of this paper to discuss a construction of right arithmetical (or right D-domains in [5]) domains, i.e., integral domains R for which the lattice of right ideals is distributive (see also [3]). Whereas the commutative rings in this class are precisely the Prüfer domains, not even right and left principal ideal domains are necessarily arithmetical. Among other things we show that a Bezout domain is right arithmetical if and only if all maximal right ideals are two-sided.Any right ideal of a right noetherian, right arithmetical domain is two-sided. This fact makes it possible to describe the semigroup of right ideals in such a ring in a satisfactory way; [3], [5].
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Karamsi, Jayalakshmi. "The ideals in (-1,1) rings." International Journal of Algebra and Statistics 3, no. 1 (June 6, 2014): 22. http://dx.doi.org/10.20454/ijas.2014.816.
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A (-1, 1) ring \(R\) contains a maximal ideal \(I_{3}\) in the nucleus \(N\). The set of elements \(n\) in the nucleus which annihilates the associators in (-1, 1) ring \(R\), \(n(x, y, z) = 0\) and \((x, y, z)n = 0\) for all \(x, y, z \in R\) form the ideal \(I_{3}\) of \(R\). Let \(I\) be a right ideal of a 2-torsion free (-1, 1) ring \(R\) with commutators in the middle nucleus. If \(I\) is maximal and nil, then \(I\) is a two sided ideal. Also if \(I\) is minimal then it is either a two-sided ideal, or the ideal it generates is contained in the middle nucleus of \(R\) and the radical of \(R\) is contained in \(P\) for any primitive ideal \(p\) of \(R\).
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CHATTERS, A. W., C. R. HAJARNAVIS, and R. M. LISSAMAN. "PROJECTIVE PRIME IDEALS AND LOCALISATION IN PI-RINGS." Journal of the London Mathematical Society 64, no. 1 (August 2001): 1–12. http://dx.doi.org/10.1017/s0024610701002125.
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The results here generalise [2, Proposition 4.3] and [9, Theorem 5.11]. We shall prove the following.THEOREM A. Let R be a Noetherian PI-ring. Let P be a non-idempotent prime ideal of R such that PRis projective. Then P is left localisable and RPis a prime principal left and right ideal ring.We also have the following theorem.THEOREM B. Let R be a Noetherian PI-ring. Let M be a non-idempotent maximal ideal of R such that MRis projective. Then M has the left AR-property and M contains a right regular element of R.
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Xu, Xiaowei, Jing Ma, and Fengwen Niu. "Generalized Derivations Having the Same Power Values with Left Multiplications." Algebra Colloquium 20, no. 03 (July 4, 2013): 369–82. http://dx.doi.org/10.1142/s1005386713000345.
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Let R be a prime ring with extended centroid C, maximal right ring of quotients U, a nonzero ideal I and a generalized derivation δ. Suppose δ(x)n =(ax)n for all x ∈ I, where a ∈ U and n is a fixed positive integer. Then δ(x)=λax for some λ ∈ C. We also prove two generalized versions by replacing I with a nonzero left ideal [Formula: see text] and a noncommutative Lie ideal L, respectively.
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Mendes-Gonçalves, Suzana, and R. P. Sullivan. "The Ideal Structure of Semigroups of Linear Transformations with Lower Bounds on Their Nullity or Defect." Algebra Colloquium 17, no. 01 (March 2010): 109–20. http://dx.doi.org/10.1142/s1005386710000131.
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Suppose V is an infinite-dimensional vector space and let T(V) denote the semigroup (under composition) of all linear transformations of V. In this paper, we study the semigroup OM(p,q) consisting of all α ∈ T(V) for which dim ker α ≥ q and the semigroup OE(p,q) of all α ∈ T(V) for which codim ran α ≥ q, where dim V = p ≥ q ≥ ℵ0. It is not difficult to see that OM(p,q) and OE(p,q) are a right ideal and a left ideal of T(V), respectively, and using these facts, we show that they belong to the class of all semigroups whose sets of bi-ideals and quasi-ideals coincide. Also, we describe Green's relations and the two-sided ideals of each semigroup, and determine its maximal regular subsemigroup. Finally, we determine some maximal right cancellative subsemigroups of OE(p,q).
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Hajarnavis, C. R. "One sided invertibility and localisation." Glasgow Mathematical Journal 34, no. 3 (September 1992): 333–39. http://dx.doi.org/10.1017/s0017089500008909.
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In general, a prime ideal P of a prime Noetherian ring need not be classically localisable. Since such a localisation, when it does exist, is a striking property; sufficiency criteria which guarantee it are worthy of careful study. One such condition which ensures localisation is when P is an invertible ideal [5, Theorem 1.3]. The known proofs of this result utilise both the left as well as the right invertiblity of P. Such a requirement is, in practice, somewhat restrictive. There are many occasions such as when a product of prime ideals is invertible [6] or when a non-idempotent maximal ideal is known to be projective only on one side [2], when the assumptions lead to invertibilty also on just one side. Our main purpose here is to show that in the context of Noetherian prime polynomial identity rings, this one-sided assumption is enough to ensure classical localisation [Theorem 3.5]. Consequently, if a maximal ideal in such a ring is invertible on one side then it is invertible on both sides [Proposition 4.1]. This result plays a crucial role in [2]. As a further application we show that for polynomial identity rings the definition of a unique factorisation ring is left-right symmetric [Theorem 4.4].
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K.V.Naga Lakshmi, N.Srimannarayana, Srinivas Telikepalli, A. Gangadhara Rao,. "Fuzzy Simple Partially Ordered Γ- Semigroups." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 5 (April 11, 2021): 842–45. http://dx.doi.org/10.17762/turcomat.v12i5.1492.
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In this paper, it is shown that and are respectively fuzzy left and fuzzy right ideals of S. S is a fuzzy left(right) simple po- Γ -semigroup ( ) .
It is proved that for any semi group S “TFAE”
(1) S is left(right) simple po- Γ -semigroup.
(2) S is a fuzzy left(right)simple Γ-semigroup.
The union of all proper fuzzy ideals of S is the only fuzzy maximal ideal of S ,where S is a PO -Γ-Semigroupwith 'e', unity.
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Hosny, Mona. "Generalization of rough sets using maximal right neighborhood systems and ideals with medical applications." AIMS Mathematics 7, no. 7 (2022): 13104–38. http://dx.doi.org/10.3934/math.2022724.
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<abstract><p>Rough set theory is a mathematical technique to address the issues of uncertainty and vagueness in knowledge. An ideal is considered to be a crucial extension of this theory. It is an efficacious tool to dispose of vagueness and uncertainties by helping us to approximate the rough set in a more general manner. Minimizing the boundary region is one of the pivotal and substantial themes for studying the rough sets which consequently aim to maximize the accuracy measure. An ideal is one of the effective and successful followed methods to achieve this goal perfectly. So, the objective of this work is to present new methods for rough sets by using ideals. Some important characteristics of these methods are scrutinized and demonstrated to show that they yield accuracy measures greater and higher than the former ones in the other approaches. Finally, two medical applications are introduced to show the significance of utilizing the ideals in the proposed methods.</p></abstract>
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Marisetti Sowjanya, Radha Rani Tammileti, Gangadhara Rao Ankata,. "f-Primary Ideals in Semigroups." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 5 (April 11, 2021): 857–61. http://dx.doi.org/10.17762/turcomat.v12i5.1495.
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Right now, the terms left f-Primary Ideal, right f-Primary Idealand f- primary ideals are presented. It is Shown that An ideal U in a semigroup S fulfills the condition that If G, H are two ideals of S with the end goal that f (G) f (H)⊆U and f(H)⊈U then f(G)⊆rf (U)iff f (q), f (r)⊆S , <f (q)><f (r)>⊆U and f (r)⊈U then f (q)⊆rf (U) in like manner it is exhibited that An ideal U out of a semigroup S fulfills condition If G, H are two ideals of S such that f (G) f (H)⊆U and f (G)⊈U then f (H) ⊆rf (U) iff f (q), f (r)⊆S,<f (q)><f (r)>⊆U and f (q)⊈U⇒f (r)⊆rf (U). By utilizing the meanings of left - f- primary and right f- primary ideals a couple of conditions are illustrated It is shown that J is a restrictive maximal ideal in Son the off chance thatrf (U) = J for some ideal U in S at that point J will be a f- primary ideal and Jn is f-primary ideal for some n it is explained that if S is quasi-commutative then an ideal U of S is left f - primary iff right f -primary.
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Hashemi, Ebrahim, Fatemeh Shokuhifar, and Abdollah Alhevaz. "On quasi-radical of near-ring of polynomials." Studia Scientiarum Mathematicarum Hungarica 56, no. 2 (June 2019): 252–59. http://dx.doi.org/10.1556/012.2019.56.2.1430.
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Abstract The intersection of all maximal right ideals of a near-ring N is called the quasi-radical of N. In this paper, first we show that the quasi-radical of the zero-symmetric near-ring of polynomials R0[x] equals to the set of all nilpotent elements of R0[x], when R is a commutative ring with Nil (R)2 = 0. Then we show that the quasi-radical of R0[x] is a subset of the intersection of all maximal left ideals of R0[x]. Also, we give an example to show that for some commutative ring R the quasi-radical of R0[x] coincides with the intersection of all maximal left ideals of R0[x]. Moreover, we prove that the quasi-radical of R0[x] is the greatest quasi-regular (right) ideal of it.
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Özcan, A. Çiğdem, and Pınar Aydoğdu. "A Generalization of Semiregular and Almost Principally Injective Rings." Algebra Colloquium 17, spec01 (December 2010): 905–16. http://dx.doi.org/10.1142/s1005386710000842.
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In this article, we call a ring R right almost I-semiregular for an ideal I of R if for any a ∈ R, there exists a left R-module decomposition lRrR(a) = P ⊕ Q such that P ⊆ Ra and Q ∩ Ra ⊆ I, where l and r are the left and right annihilators, respectively. This generalizes the right almost principally injective rings defined by Page and Zhou, I-semiregular rings defined by Nicholson and Yousif, and right generalized semiregular rings defined by Xiao and Tong. We prove that R is I-semiregular if and only if for any a ∈ R, there exists a decomposition lRrR(a) = P ⊕ Q, where P = Re ⊆ Ra for some e2 = e ∈ R and Q ∩ Ra ⊆ I. Among the results for right almost I-semiregular rings, we show that if I is the left socle Soc (RR) or the right singular ideal Z(RR) or the ideal Z(RR) ∩ δ(RR), where δ(RR) is the intersection of essential maximal left ideals of R, then R being right almost I-semiregular implies that R is right almost J-semiregular for the Jacobson radical J of R. We show that δl(eRe) = e δ(RR)e for any idempotent e of R satisfying ReR = R and, for such an idempotent, R being right almost δ(RR)-semiregular implies that eRe is right almost δl(eRe)-semiregular.
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Hajarnavis, C. R. "One sided invertibility and localisation II." Glasgow Mathematical Journal 37, no. 1 (January 1995): 15–19. http://dx.doi.org/10.1017/s0017089500030330.
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The aim of this paper is to generalise the results of [7] from the prime to the semiprime case. It was shown, for instance, that if M is the annihilator of a simple right module S of projective dimension 1 over a Noetherian prime polynomial identity (PI) ring R then M is either an invertible ideal or an idempotent ideal [7, Proposition 4.2]. One of the main applications of this result was that a prime Noetherian affine PI ring of global dimension less than or equal to 2 is a finite module over its centre. It turns out that this theorem is valid more generally when the ring is semiprime [1, Theorem A]. Clearly this requires [7, Proposition 4.2] also to be strengthened to the semiprime case. We do this by showing that a right invertible maximal ideal in a semiprime Noetherian PI ring is also left invertible (Theorem 3.5).
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Hirano, Yasuyuki, Jae Keol Park, and Klaus W. Roggenkamp. "Global dimension of factor rings." Bulletin of the Australian Mathematical Society 49, no. 3 (June 1994): 399–411. http://dx.doi.org/10.1017/s0004972700016506.
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Let R be a right Noetherian ring with right global dimension bounded by 2, which is integral over its centre, and let a be a regular non-unit element in R. Then R/a; R is right hereditary if and only if a; is not in the square of any maximal ideal of R. More generally, we compare for a right Noetherian ring R which is integral over its center, the global dimension of R with the global dimension of R/(a1R + a2R + … + arR) for a regular R-sequence {ai}, which will allow us to give a considerable extension of a result of Hillman.
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Whelan, E. A. "Bi-artinian noetherian rings." Glasgow Mathematical Journal 43, no. 1 (January 2001): 9–21. http://dx.doi.org/10.1017/s0017089501010023.
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A noetherian ring R satisfies the descending chain condition on two-sided ideals (“is bi-artinian”) if and only if, for each prime P ∈ spec(R), R/P has a unique minimal ideal (necessarily idempotent and left-right essential in R/P). The analogous statement for merely right noetherian rings is false, although our proof does not use the full noetherian condition on both sides, requiring only that two-sided ideals be finitely generated on both sides and that R/Q be right Goldie for each Q ∈ spec(R). Examples exist, for each n∈ℕ and in all characteristics, of bi-artinian noetherian domains Dn with composition series of length 2n and with a unique maximal ideal of height n. Noetherian rings which satisfy the related E-restricted bi-d.c.c. do not, in general, satisfy the second layer condition (on either side), but do satisfy the Jacobson conjecture.
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Van Huynh, Dinh, Nguyen V. Dung, and Patrick F. Smith. "Rings characterized by their right ideals or cyclic modules." Proceedings of the Edinburgh Mathematical Society 32, no. 3 (October 1989): 355–62. http://dx.doi.org/10.1017/s0013091500004612.
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It is well known that a ring R is semiprime Artinian if and only if every right ideal is an injective right R-module. In this paper we shall be concerned with the following general question: given a ring R all of whose right ideals have a certain property, what implications does this have for the ring R itself? In practice, it is not necessary to insist that all right ideals have the property, usually the maximal or essential right ideals will suffice. On the other hand, Osofsky proved that a ring R is semiprime Artinian if and only if every cyclic right R-module is injective. This leads to the second general question: given a ring R all of whose cyclic right R-modules have a certain property, what can one say about R itself?
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Chatters, A. W., and M. M. Parmenter. "Stably Free Modules Over Rings of Generalised Integer Quaternions." Canadian Mathematical Bulletin 38, no. 4 (December 1, 1995): 408–11. http://dx.doi.org/10.4153/cmb-1995-059-5.
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AbstractIn this note, we obtain, in a rather easy way, examples of stably free non-free right ideals. We also give an example of a stably free non-free two-sided ideal in a maximal ℤ-order. These are obtained as applications of a theorem giving necessary and sufficient conditions for H/nH to be a complete 2 x 2 matrix ring, when H is a generalised quaternion ring.
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Chatters, A. W., M. P. Gilchrist, and D. Wilson. "Unique factorisation rings." Proceedings of the Edinburgh Mathematical Society 35, no. 2 (June 1992): 255–69. http://dx.doi.org/10.1017/s0013091500005526.
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Let R be a ring. An element p of R is a prime element if pR = Rp is a prime ideal of R. A prime ring R is said to be a Unique Factorisation Ring if every non-zero prime ideal contains a prime element. This paper develops the basic theory of U.F.R.s. We show that every polynomial extension in central indeterminates of a U.F.R. is a U.F.R. We consider in more detail the case when a U.F.R. is either Noetherian or satisfies a polynomial identity. In particular we show that such a ring R is a maximal order, that every height-1 prime ideal of R has a classical localisation in which every two-sided ideal is principal, and that R is the intersection of a left and right Noetherian ring and a simple ring.
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Baker, J. W., and A. T. Lau. "Compact left ideal groups in semigroup compactification of locally compact groups." Mathematical Proceedings of the Cambridge Philosophical Society 113, no. 3 (May 1993): 507–17. http://dx.doi.org/10.1017/s0305004100076167.
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Let G be a locally compact group and let UG denote the spectrum of the C*-algebra LUC(G) of bounded left uniformly continuous complex-valued functions on G, with the Gelfand topology. Then there is a multiplication on UG extending the multiplication on G (when naturally embedded in UG) such that UG is a semigroup and for each x ∈ UG, the map y ↦ yx from UG into UG is continuous, i.e. UG is a compact right topological semigroup. Consequently UG has a unique minimal ideal K which is the union of minimal (closed) left ideals UG. Furthermore K is the union of the set of maximal subgroups of K (see [3], theorem 3·ll).
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López-Permouth, Sergio R., K. P. Shum, and Nguyen Van Sanh. "Kasch Modules and pV-Rings." Algebra Colloquium 12, no. 02 (June 2005): 219–27. http://dx.doi.org/10.1142/s1005386705000210.
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Let R be a ring. A right R-module M is called p-injective if every homomorphism from a principal right ideal of R to M can be given by a left multiplication. A ring R is called a right pV-ring if every simple R-module is p-injective. In this paper, Kasch modules are considered. It is proved that if a Kasch module M is finitely generated and quasi-p-injective, then there is a bijective correspondence between the class of maximal submodules of M and the class of all minimal left ideals of its endomorphism ring. Also, it is proved that if M is a pV-module which is a finitely generated projective self-generator, then its endomorphism ring is a right pV-ring. Finally, it is proved that being a right or left pV-ring is a Morita invariant.
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KIM, JU MYUNG. "SOME RESULTS OF THE -APPROXIMATION PROPERTY FOR BANACH SPACES." Glasgow Mathematical Journal 61, no. 03 (August 9, 2018): 545–55. http://dx.doi.org/10.1017/s0017089518000356.
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AbstractGiven a Banach operator ideal $\mathcal A$, we investigate the approximation property related to the ideal of $\mathcal A$-compact operators, $\mathcal K_{\mathcal A}$-AP. We prove that a Banach space X has the $\mathcal K_{\mathcal A}$-AP if and only if there exists a λ ≥ 1 such that for every Banach space Y and every R ∈ $\mathcal K_{\mathcal A}$(Y, X), $$ \begin{equation} R \in \overline {\{SR : S \in \mathcal F(X, X), \|SR\|_{\mathcal K_{\mathcal A}} \leq \lambda \|R\|_{\mathcal K_{\mathcal A}}\}}^{\tau_{c}}. \end{equation} $$ For a surjective, maximal and right-accessible Banach operator ideal $\mathcal A$, we prove that a Banach space X has the $\mathcal K_{(\mathcal A^{{\rm adj}})^{{\rm dual}}}$-AP if the dual space of X has the $\mathcal K_{\mathcal A}$-AP.
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Vladeva, Dimitrinka. "Projections on right and left ideals of endomorphism semiring which are derivations." Journal of Algebra and Its Applications 19, no. 11 (November 1, 2019): 2050212. http://dx.doi.org/10.1142/s0219498820502126.
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The aim of this paper is the investigation of the derivations in an endomorphism semiring of a finite chain. Such semiring can be represented as a simplex and its subsimplices are left ideals of the semiring. We construct projections on these left ideals and prove that they are derivations and also find the maximal subsemirings of the simplex which are the domains of the constructed derivations. Consequently, we obtain some results concerning nilpotent endomorphisms and using well-known result of Stanley we prove that order of semiring of nilpotent endomorphisms is equal to [Formula: see text], where [Formula: see text] is the [Formula: see text]th Catalan number. We consider a class of right ideals of the semiring and introduce projections on these ideals which are derivations and also find the maximal subsemirings of the simplex which are the domains of the constructed derivations. For one of these derivations [Formula: see text] and for a fixed endomorphism [Formula: see text] of a considered right ideal, the set of endomorphisms [Formula: see text] such that [Formula: see text] is denoted by [Formula: see text]. The last set is a semiring if and only if [Formula: see text] is an idempotent. The number of the semirings [Formula: see text], where [Formula: see text], is equal to [Formula: see text], which is the [Formula: see text]th Fibonacci number.
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Mahmood, Raida D., and Khedher J. Khider. "On P Wπ-regular rings." Journal of Physics: Conference Series 1591, no. 1 (July 1, 2020): 012098. http://dx.doi.org/10.1088/1742-6596/1591/1/012098.
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Abstract As a popularization of weakly π-regular rings, we tender the connotation of W P Wπ-regular rings, that is if for each 𝔞 ∈ Ɉ(𝔑), there exist a natural number 𝔫 such that 𝔞𝔫 ∈ 𝔞𝔫 𝔑 𝔞𝔫 𝔑 (𝔞𝔫 ∈ 𝔑 𝔞𝔫 𝔑 𝔞𝔫). In this treatise, numerous properties of this sort of rings are discussed, some important results are secured. Using the connotation of P Wπ-regular rings. It is show that : 1- Let 𝔑 be a right P Wπ-regular ring and ℵɈ-rings with 𝔞𝔫𝔑 = 𝔑𝔞𝔫 for every 𝔞 ∈ Ɉ(𝔑) and for at least one of a natural number. Then Ɉ(𝔑) = ℵ𝔑. 2- Let 𝔑 a right P Wπ-regular ring and 𝔞𝔑 = 𝔑𝔞 for each ∈Ɉ(𝔑). Then 𝔑 is right P .𝔗-ring. 3 Let 𝔑 be a ring with ɍ(𝔞) ⊆ ɭ(𝔞), for each ∈ Ɉ (𝔑). If any of the next conditions are hold, then 𝔑 is P Wπ-regular rings : i – Every maximal right ideal of 𝔑 is a right annihilator and right Ɉ PP -ring. ii – any simple singular right 𝔑-module is Ɉ-injective and 𝔑 is semi prime.
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Mahjoub, Haïfa, Olivier Le Blanc, Myriam Paquette, Sarah Imhoff, Lawrence Labrecque, Audrey Drapeau, Paul Poirier, Élisabeth Bédard, Philippe Pibarot, and Patrice Brassard. "Cardiac remodeling after six weeks of high-intensity interval training to exhaustion in endurance-trained men." American Journal of Physiology-Heart and Circulatory Physiology 317, no. 4 (October 1, 2019): H685—H694. http://dx.doi.org/10.1152/ajpheart.00196.2019.
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High-intensity interval training (HIIT) improves physical performance of endurance athletes, although studies examining its cardiovascular effects are sparse. We evaluated the impact of HIIT on blood pressure, heart rate, and cardiac cavities’ size and function in endurance-trained adults. Seventeen endurance-trained men underwent 24-h ambulatory blood pressure monitoring and Doppler echocardiography at baseline and after 6 wk of HIIT. Participants were divided into 2 groups [85% maximal aerobic power (HIIT85), n = 8 and 115% maximal aerobic power (HIIT115), n = 9] to compare the impact of different HIIT intensities. Ambulatory blood pressure monitoring and cardiac chambers’ size and function were similar between groups at baseline. HIIT reduced heart rate (55 ± 8 vs. 51 ± 7 beats/min; P = 0.003), systolic blood pressure (121 ± 11 vs. 118 ± 9 mmHg; P = 0.01), mean arterial pressure (90 ± 8 vs. 89 ± 6 mmHg; P = 0.03), and pulse pressure (52 ± 6 vs. 49 ± 5 mmHg; P = 0.01) irrespective of training intensity. Left atrium volumes increased after HIIT (maximal: 50 ± 14 vs. 54 ± 14 mL; P = 0.02; minimal: 15 ± 5 vs. 20 ± 8 mL; P = 0.01) in both groups. Right ventricle global longitudinal strain lowered after training in the HIIT85 group only (20 ± 4 vs. 17 ± 3%, P = 0.04). In endurance-trained men, 6 wk of HIIT reduced systolic blood pressure and mean arterial pressure and increased left atrium volumes irrespective of training intensity, whereas submaximal HIIT deteriorated right ventricle systolic function. NEW & NOTEWORTHY The novel findings of this study are that 6 wk of high-intensity interval training increases left atrial volumes irrespective of training intensity (85 or 115% maximal aerobic power), whereas the submaximal training decreases right ventricular systolic function in endurance-trained men. These results may help identify the exercise threshold for potential toxicity of intense exercise training for at-risk individuals and ideal exercise training regimens conferring optimal cardiovascular protection and adapted endurance training for athletes.
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Patil, Nikita, Pooja Patil, Abhishek Patil, and Shraddha N. Bhavasar. "MICROSPHERES: A NOVEL DRUG DELIVERYSYSTEM." International Journal of Advanced Research 9, no. 12 (December 31, 2021): 903–22. http://dx.doi.org/10.21474/ijar01/13990.
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Microspheres are freeflowing powders that are made up of proteins or synthetic polymers. They are little spherical particles with diameters ranging from a few millimetres to a few millimetres (typically from 1 to 100 micrometer). Microspheres are microparticles that are employed in applications that require a predictable and constant particle surface area.To achieve the desired impact, the drug should be delivered in an ideal amount at the right time to the target tissue with the least degree of adverse effects and maximal therapeutic efficacy. The microspheres drew a lot of attention because of their long-lasting release and ability to target anticancermedications to the tumor.Microspheres will play a key role in innovative medication delivery in the future, particularly in sick cell sorting, diagnostics, gene & genetic materials, and safe, targeted and precise delivery.
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Sharma, Ram Parkash, Richa Sharma, and Madhu. "Radicals of semirings." Asian-European Journal of Mathematics 13, no. 07 (August 6, 2019): 2050138. http://dx.doi.org/10.1142/s1793557120501387.
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It is shown that the classes [Formula: see text] and [Formula: see text] of semirings are radical classes, where [Formula: see text] is the class of subtractive-simple right [Formula: see text]-semimodules and [Formula: see text] is the class of right [Formula: see text]-semimodules isomorphic to [Formula: see text] for some maximal-subtractive right ideal [Formula: see text] of [Formula: see text]. We define the lower Jacobson Bourne radical [Formula: see text] and upper Jacobson Bourne radical [Formula: see text] of [Formula: see text]. For a semiring [Formula: see text], [Formula: see text] holds, where [Formula: see text] is the Jacobson Bourne radical of [Formula: see text]. The radical [Formula: see text] and also coincides with [Formula: see text], if we restrict the class [Formula: see text] to additively cancellative semimodules[Formula: see text] The upper radical [Formula: see text] and [Formula: see text][Formula: see text], if [Formula: see text] is additively cancellative. Further, [Formula: see text], if [Formula: see text] is a commutative semiring with [Formula: see text] The subtractive-primitiveness and subtractive-semiprimitiveness of [Formula: see text] are closely related to the upper radical [Formula: see text] Finally, we show that [Formula: see text]-semisimplicity of semirings are Morita invariant property with some restrictions.
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Elavenil, P., S. Mohanavalli, B. Sasikala, R. Ashok Prasanna, and Raja V. B. Krishnakumar. "Isolated Bilateral Mandibular Angle Fractures: An Extensive Literature Review of the Rare Clinical Phenomenon with Presentation of a Classical Clinical Model." Craniomaxillofacial Trauma & Reconstruction 8, no. 2 (June 2015): 153–58. http://dx.doi.org/10.1055/s-0034-1393738.
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Bilateral angle fractures are a rare clinical phenomenon in contrast to the incidence of unilateral angle fractures. However, the rarity has garnered less attention in spite of the uniqueness of fracture pattern and distinctive biomechanics. This article is a detailed review on the etiology, clinical presentation, and management of bilateral angle fractures with the presentation of an interesting case. The bilateral angle fracture reported is a untreated, malunited fracture representing an ideal clinical model to study its biomechanics. The clinical features were anterior open bite, increased facial height, and temporomandibular joint tenderness. The management included osteotomy at the malunion and miniplate osteosynthesis. Bilateral angle fracture presents mandible in three independent fragments (left angle, right angle, and intermediate corpus), each with strong muscles acting in different vectors. This makes the fracture vulnerable to severe displacing forces and unfavorable to achieve the optimal reduction, stability, and healing. This necessitates comprehension of the biomechanical forces involved to avoid malunion following fixation. The article details the complex biomechanics of mandibular angle and its clinical implications in the rare event of bilateral angle fractures. It describes the necessity for a systematic approach and ideal osteosynthesis principles to achieve maximal treatment outcomes and minimal complications.
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Gonzalez Corcia, M. Cecilia, Lorraine Saint Remy, Sebastien Marchandise, and Stephane Moniotte. "Exercise performance in young patients with complete atrioventricular block: the relevance of synchronous atrioventricular pacing." Cardiology in the Young 26, no. 6 (January 22, 2016): 1066–71. http://dx.doi.org/10.1017/s104795111500178x.
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AbstractAt present, there are many pacing strategies for young patients with complete atrioventricular block. The most frequent policy is to attempt placing a dual-chamber system when possible; however, there is a group of patients that is functioning with a non-synchronous ventricular pacing, raising the question of the ideal timing to upgrade their systems. We investigated the exercise performance of a group of children and young adults with complete atrioventricular block and dual-chamber pacemakers in both single- and dual-chamber pacing modalities. A total of 15 patients performed maximal exercise stress testing after programming the VVIR or DDD modes with 2 hours of interval in a double-blind study protocol.Compared with VVIR pacing, DDD pacing resulted in increase in the peak VO2, longer test duration, major increase in the heart rate achieved during peak exercise, decreased systemic non-invasive arterial blood pressure measured at maximal exercise, higher maximal workload, prolongation of the anaerobic threshold timing, and better self-rated performance perception in all the patients.Synchronous atrioventricular pacing contributes to an increase in both the exercise performance and the performance perception in 100% of the patients. This difference contributes to create a sense of “fitness” with repercussions in the overall health, self-esteem, and life quality, as well as encourages youngster to practice sports. Our experience tends to favour upgrading patients’ systems to dual-chamber systems before reaching the adolescent years, even if the centre policy is to prolong as long as possible the epicardial site in order to avoid long years of right ventricular pacing.
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Bhardwaj, Praveen, Saumyakumar S. Nayak, Asif M. Kiswar, and S. Raja Sabapathy. "Effect of static wrist position on grip strength." Indian Journal of Plastic Surgery 44, no. 01 (January 2011): 055–58. http://dx.doi.org/10.1055/s-0039-1699481.
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ABSTRACT Background: Grip strength after wrist arthrodesis is reported to be significantly less than normal. One of the reasons suggested for this decrease in grip strength is that the arthrodesis was performed in a suboptimal position. However, there is no consensus on the ideal position of wrist fusion. There is a paucity of studies evaluating the effect of various fixed positions of the wrist on grip strength and therefore, there is no guide regarding the ideal position of wrist fusion. The authors’ aim was to determine the grip strength in various fixed positions of the wrist and subsequently to find out in which position of wrist fusion the grip strength would be maximal. Materials and Methods: One hundred healthy adults participated in the study. For the purpose of this study, the authors constructed splints to hold the wrist in five different fixed positions: 45, 30 and 15 degrees of wrist extension, neutral and 30 degrees of wrist flexion. The grip strength in all the participants was measured bilaterally, first without a splint and then with each splint sequentially. Results: The average grip strength without the splint was 34.3 kg for right and 32.3 kg for the left hand. Grip strength decreased by 19–25% when the wrist was splinted. The maximum average grip strength with a splint on was recorded at 45 degrees of extension (27.9 kg for right and 26.3 kg for left side). There was a gradual increase in the grip strength with increase in wrist extension but the difference was not statistically significant (P = 0.29). The grip strength was significantly less in flexed position of the wrist (P < 0.001).
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Solecki, Sławomir. "Analytic Ideals." Bulletin of Symbolic Logic 2, no. 3 (September 1996): 339–48. http://dx.doi.org/10.2307/420994.
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§1. Introduction. Ideals and filters of subsets of natural numbers have been studied by set theorists and topologists for a long time. There is a vast literature concerning various kinds of ultrafilters (or, dually, maximal ideals). There is also a substantial interest in nicely definable (Borel, analytic) ideals—these by old results of Sierpiński are very far from being maximal— and the structure of such ideals will concern us in this announcement. In addition to being interesting in their own right, Borel and analytic ideals occur naturally in the investigations of compact subsets of the space of all Baire class 1 functions on a Polish space (Rosenthal compacta), see [12, 18]. Also, certain objects associated with such ideals are of considerable interest and were quite extensively studied by several authors. Let us list here three examples; in all three of them I stands for an analytic or Borel ideal.1. The partial order induced by I on P(ω): X ≥I Y iff X \ Y ϵ I ([16]) and the partial order (I, ⊂)([18]).2. Boolean algebras of the form P(ω)/I and their automorphisms ([6, 5, 19, 20]).3. The equivalence relation associated with I: XEI Y iff X Δ ϵ I ([4, 14, 15,9]).In Section 4, we will have an opportunity to state some consequences of our results for equivalence relations as in 3.
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Rochmah, Yayun Siti. "OSTEORADIONEKROSIS PASCA EKSTRAKSI GIGI PASIEN DENGAN RIWAYAT KANKER NASOFARING." ODONTO : Dental Journal 6, no. 1 (April 22, 2019): 19. http://dx.doi.org/10.30659/odj.6.1.19-22.
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Background: Osteoradionecrosis (ORN) post dental extraction is post dentalextraction complication with post radiation cancer theraphy. Objective : to present rare case, ORN post dental extraction with post radiation Ca nasopharing therapy 3 years ago.Case Management: A 54 years old patient reported to the dental out-patient department with a chief complaint of pus discharge from right buccal since post dental extraction 6 months ago. He gave a history of a nasopharing Carcinoma with histopatology as squamous cell carcinoms 3 years ago and radio therapy but no surgery. Intraoral examination, exposed necrotic bone found from right lower retromolar area 46 with pus discharge. Radiographic view was likely squester. Local surgical debridement and the sequestrectomy was undertaken with general anaesthesia. Antibiotic injection treatment was ceftriaxon 2x 1gram, infus metronidazol 3x500 mg and ketorolac 3x1 ampul, the patient was treated for 3 days and educated to maintain his oral hygiene with povidone iodine gargle.Discussion: Osteoradionecrosis (ORN) is late effect of radiation therapy thatresults in irreversible tissue death, which is clinically observed as bony exposure for more than 3 months duration. The mandible is affected more often than the maxilla or any other bones of head and neck region. The incidence of ORN in the mandible is reported to be between 2% and 22% and most often affects the body of the mandible. Ideal time is one year minimal post radiotherapy to get maximal vascularization for optimal healing. But immunity factor and radiation doses can trigger emergense ORN.Conclusion: Need time consideration, clinic analysis and pathologys before doing dental extraction for post radiotherapy cancer cases to prevent ORN.
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ALI-AKBARI, M., B. HONARI, M. POURMAHDIAN, and M. M. REZAII. "The space of formal balls and models of quasi-metric spaces." Mathematical Structures in Computer Science 19, no. 2 (April 2009): 337–55. http://dx.doi.org/10.1017/s0960129509007439.
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In this paper we study quasi-metric spaces using domain theory. Our main objective in this paper is to study the maximal point space problem for quasi-metric spaces. Here we prove that quasi-metric spaces that satisfy certain completeness properties, such as Yoneda and Smyth completeness, can be modelled by continuous dcpo's. To achieve this goal, we first study the partially ordered set of formal balls (BX, ⊑) of a quasi-metric space (X, d). Following Edalat and Heckmann, we prove that the order properties of (BX, ⊑) are tightly connected to topological properties of (X, d). In particular, we prove that (BX, ⊑) is a continuous dcpo if (X, d) is algebraic Yoneda complete. Furthermore, we show that this construction gives a model for Smyth-complete quasi-metric spaces. Then, for a given quasi-metric space (X, d), we introduce the partially ordered set of abstract formal balls (BX, ⊑, ≺). We prove that if the conjugate space (X, d−1) of a quasi-metric space (X, d) is right K-complete, then the ideal completion of (BX, ⊑, ≺) is a model for (X, d). This construction provides a model for any Yoneda-complete quasi-metric space (X, d), as well as the Sorgenfrey line, Kofner plane and Michael line.
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Corson, Jon M., and Lance L. Ross. "Automata with Counters that Recognize Word Problems of Free Products." International Journal of Foundations of Computer Science 26, no. 01 (January 2015): 79–98. http://dx.doi.org/10.1142/s0129054115500045.
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An M-automaton is a finite automaton with a blind counter that mimics a monoid M. The finitely generated groups whose word problems (when viewed as formal languages) are accepted by M-automata play a central role in understanding the family 𝔏(M) of all languages accepted by M-automata. If G1 and G2 are finitely generated groups whose word problems are languages in 𝔏(M), in general, the word problem of the free product G1 * G2 is not necessarily in 𝔏(M). However, we show that if M is enlarged to the free product M*P2, where P2 is the polycyclic monoid of rank two, then this closure property holds. In fact, we show more generally that the special word problem of M1 * M2 lies in 𝔏(M * P2) whenever M1 and M2 are finitely generated monoids with special word problems in 𝔏(M * P2). We also observe that there is a monoid without zero, denoted by CF2, that can be used in place of P2 for this purpose. The monoid CF2 is the rank two case of what we call a monoid with right invertible basis and its Rees quotient by its maximal ideal is P2. The fundamental theory of monoids with right invertible bases is completely analogous to that of free groups, and thus they are very convenient to use. We also investigate the questions of whether there is a group that can be used instead of the monoid P2 in the above result and under what circumstances P1 (or the bicyclic monoid) is enough to do the job of P2.
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Manigos, Kirby, Kevin Paul Ferraris, Joseph Erroll Navarro, Kenny Seng, and Jose Carlos Alcazaren. "SURG-08. AWAKE CRANIOTOMY WITH BRAIN MAPPING FOR DIFFUSE LOW-GRADE GLIOMA: CASE REPORT OF INSTITUTIONAL EXPERIENCE IN OVERCOMING HURDLES IN A LOW-RESOURCE SETTING." Neuro-Oncology 22, Supplement_2 (November 2020): ii204—ii205. http://dx.doi.org/10.1093/neuonc/noaa215.855.
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Abstract Maximal safe resection of low-grade gliomas located in functional areas of the cortex while avoiding postsurgical neurologic deficits can be achieved by awake craniotomy with brain mapping. The effectiveness of this surgical technique is fairly established in the developed world, however it remains to be routinely applied in low-middle income countries due to limited resources and lack of equipment. We present the case of a 44 year-old, right-handed male who had a 2-year history of focal aware motor seizures but was otherwise neurologically intact. Neuropsychological testing revealed no cognitive impairment. Cranial magnetic resonance imaging (MRI) revealed a non-enhancing, ill-defined tumor centered on the left insula and extending into the frontotemporal opercula, corona radiata, and posterior limb of the internal capsule—hypointense by T1-weighted sequence and hyperintense by T2-weighted sequence, thus radiographically consistent with diffuse low-grade glioma. Blood-oxygen-level-dependent functional MRI revealed left hemispheric language dominance in the cortex overlying the tumor, but with no motor cortex involvement. The patient underwent a protocol-driven awake craniotomy, intraoperative positive brain mapping using standard cortical stimulator, transsylvian and transcortical transopercular microsurgical approaches to achieve greater than 80% excision of the tumor. Postoperatively, the patient was seizure-free and with similar neurocognitive status prior to the surgery. The patient had been following up for standard adjuvant chemotherapy and radiotherapy. Avoidance of postsurgical neurologic deficits and maximal cytoreduction can still be achieved by awake craniotomy with brain mapping in settings with limited resources. Despite the lack of other perioperative tools and adjuncts such as diffusion tensor imaging, intraoperative ultrasonography, and even intraoperative MRI that are routinely available in high-resource settings, we illustrate in this case that comparable outcomes could be achieved by overcoming hurdles and aiming for the asymptote to the up-to-date and ideal neurosurgical treatment for diffuse low-grade gliomas.
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Chatters, A. W. "Representation of tiled matrix rings as full matrix rings." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 1 (January 1989): 67–72. http://dx.doi.org/10.1017/s0305004100001365.
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It can be very difficult to determine whether or not certain rings are really full matrix rings. For example, let p be an odd prime, let H be the ring of quaternions over the integers localized at p, and setThen T is not presented as a full matrix ring, but there is a subring W of H such that T ≅ M2(W). On the other hand, if we take H to be the ring of quaternions over the integers and form T as above, then it is not known whether T ≅ M2(W) for some ring W. The significance of p being an odd prime is that H/pH is a full 2 x 2 matrix ring, whereas H/2H is commutative. Whether or not a tiled matrix ring such as T above can be re-written as a full matrix ring depends on the sizes of the matrices involved in T and H/pH. To be precise, let H be a local integral domain with unique maximal ideal M and suppose that every one-sided ideal of H is principal. Then H/M ≅ Mk(D) for some positive integer k and division ring D. Given a positive integer n. let T be the tiled matrix ring consisting of all n x n matrices with elements of H on and below the diagonal and elements of M above the diagonal. We shall show in Theorem 2.5 that there is a ring W such that T ≅ Mn(W) if and only if n divides k. An important step in the proof is to show that certain idempotents in T/J(T) can be lifted to idempotents in T, where J(T) is the Jacobson radical of T. This technique for lifting idempotents also makes it possible to show that there are (k + n − 1)!/ k!(n−1)! isomorphism types of finitely generated indecomposable projective right T-modules (Theorem 2·10).
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Lokshin, I. M. "Democracy against Popular Sovereignty? (Faces of Power of the People: Theoretic Reconstruction)." Journal of Political Theory, Political Philosophy and Sociology of Politics Politeia 101, no. 2 (June 23, 2021): 6–29. http://dx.doi.org/10.30570/2078-5089-2020-101-2-6-29.
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In the article, on the basis of the classical political philosophers, the author distinguishes between three ideal-typical modi of political superiority of the people: “democracy”, “popular sovereignty” and “the natural right of the people to vindicate the supreme power”. Differen ces between them are drawn according to the criteria of (a) the distance between the holder of the supreme power and the holder of power that allows the routine management of the state, and (b) the degree to which the former controls the latter. The theoretic reconstruction of the modi of the political superiority of the people is based on identifying three ways to assert political superiority, expressed in the concepts of κράτος, sovereignty and vindication. This approach makes it possible to trace the specifics of each of the identified modi: “democracy” in its original (ancient Greek) sense is the power of the people, based on the obvious superiority (over the nobility) in their strength, in their excess of power, thanks to which the people are able to effectively implement their will in the public sphere; “popular sovereignty” makes the people a key political agent not by referring to their excess of power, but by securing their legal position as a source of laws and any public power; finally, “the natural right of the people to vindicate the supreme power” asserts the moral and teleological primacy of the people’s good over that of the rulers. According to the author’s conclusion, the three modi of the political superiority of the people differ from each other primarily in the extent to which the people are involved in the political process. Under “democracy” this extent is maximal, in the case of the “natural right to vindication” it is minimal, while “popular sovereignty” finds itself in the middle between these two extremes: both threats of the decisive “alienation” of the people from power and its usurpation by the “trustees” and tyranny of the people are absent. The author thinks that this middle ground of the “popular sovereignty” represents one of the reasons why it is this modus that symbolizes the architectonics of the modern democracy.
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Chamoun, Roukoz B., William E. Whitehead, Daniel J. Curry, Thomas G. Luerssen, and Andrew Jea. "Computed tomography morphometric analysis for C-1 lateral mass screw placement in children." Journal of Neurosurgery: Pediatrics 3, no. 1 (January 2009): 20–23. http://dx.doi.org/10.3171/2008.10.peds08224.
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Object The use of C-1 lateral mass screws provides an alternative to C1–2 transarticular screws in the pediatric population. However, the confined space of the local anatomy and unfamiliarity with the technique may make the placement of a C-1 lateral mass screw more challenging, especially in the juvenile or growing spine. Methods A CT morphometric analysis was performed in 76 pediatric atlases imaged at Texas Children's Hospital from October 1, 2007 until April 30, 2008. Critical measurements were determined for potential screw entry points, trajectories, and lengths, with the goal of replicating the operative technique described by Harms and Melcher for adult patients. Results The mean height and width for screw entry on the posterior surface of the lateral mass were 2.6 and 8.5 mm, respectively. The mean medially angled screw trajectory from an idealized entry point on the lateral mass was 16° (range 4 to 27°). The mean maximal screw depth from this same ideal entry point was 20.3 mm. The overhang of the posterior arch averaged 6.3 mm (range 2.1–12.4 mm). The measurement between the left- and right-side lateral masses was significantly different for the maximum medially angled screw trajectory (p = 0.003) and the maximum inferiorly directed angle (p = 0.045). Those measurements in children < 8 years of age were statistically significant for the entry point height (p = 0.038) and maximum laterally angled screw trajectory (p = 0.025) compared with older children. The differences between boys and girls were statistically significant for the minimum screw length (p = 0.04) and the anterior lateral mass height (p < 0.001). Conclusions A significant variation in the morphological features of C-1 exists, especially between the left and right sides and in younger children. The differences between boys and girls are clinically insignificant. The critical measurement of whether the C-1 lateral mass in a child could accommodate a 3.5-mm-diameter screw is the width of the lateral mass and its proximity to the vertebral artery. Only 1 of 152 lateral masses studied would not have been able to accommodate a lateral mass screw. This study reemphasizes the importance of a preoperative CT scan of the upper cervical spine to assure safe and effective placement of the instrumentation at this level.
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S. G., Mahesh, Ashwath Narayan Ramji, Balaji R., and Mali Chetan S. M. "Reconstructive strategies for lower one-third leg soft tissue defects." International Surgery Journal 5, no. 12 (November 28, 2018): 4016. http://dx.doi.org/10.18203/2349-2902.isj20185036.
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Background: Despite recent technical advances, reconstruction of lower third of leg wounds with soft tissue defects remains a challenge to the Plastic Surgeon. This is due to the inherent anatomical and structural configuration, including the limited vascularity of the skin of the lower third of the leg. Maintaining maximal function without compromising the aesthetic appearance of the leg is the goal of reconstruction.Methods: This was a retrospective study conducted in the Department of Plastic Surgery, KIMS Hospital, Bangalore, from January 2016 to January 2018. Patients with soft tissue defects involving lower third of leg requiring flap cover were included in the study. Orthopedic intervention was done as required. All patients underwent loco-regional or free flap cover as clinically indicated. Outcomes were studied.Results: Total of 20 patients were included in the study. Most common presentation was due to road traffic accidents (RTA). Right leg was involved in 12 cases and left in 8 cases. Fracture was present in 7 cases, exposed bone without fracture in 11 cases, exposed tendons alone in 1 case and exposed implants in 1 case. 3 Patients required orthopaedic intervention along with the flap procedure, and 4 had already undergone orthopaedic stabilisation. Most commonly performed procedure was muscle flap (45%), followed by perforator-based fascio-cutaneous flap (25%). No major complications were observed in the post-operative period.Conclusions: Lower third of leg reconstruction is a challenge, but a wide variety of options ranging from loco-regional to free flaps can be employed, depending on the situation. In present study, various types of flap cover were adopted to cover the lower-third of leg defects, depending on the nature of the wound. Present study delineated that muscle flaps - particularly the reverse hemi-soleus flap, are an ideal flap for lower third of leg defects with fracture site exposed and wound infected. Local muscle flaps have the advantage of being single-staged, faster to perform and technically easier, compared to free flaps, which have long been considered the gold standard.
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Parker, Mackenzie, Ayesha Zia, Tony Babb, and Michael D. Nelson. "Hemodynamic and Ventilatory Responses during Exercise in Pediatric Patients with Pulmonary Embolism." Blood 136, Supplement 1 (November 5, 2020): 9–10. http://dx.doi.org/10.1182/blood-2020-142912.
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Background Pediatric patients with pulmonary embolism (PE) suffer from exercise intolerance and dyspnea on exertion, often without right heart dysfunction or pulmonary hypertension - at least at rest. The pathophysiology of the exercise limitation following pediatric PE therefore remains incompletely understood. Objectives To extend our understanding of exercise intolerance in pediatric patients with PE by examining ventilatory and hemodynamic responses to exercise. Methods To accomplish our goal, we instituted a standardized institutional protocol to systematically assess exercise capacity in pediatric PE patients in the first 3 months following diagnosis. Between February 2019- June 2020, 15 patients underwent resting pulmonary function tests and an incremental symptom-limited cardiopulmonary exercise testing (CPET) to obtain peak exercise in 8-12 minutes. All patients had received anticoagulation for at least 3 months. In all patients, right and left ventricular systolic and/or diastolic dysfunction at rest was ruled out by transthoracic echocardiography. Continuous measurements were made of minute ventilation (VE), oxygen uptake (VO2), carbon dioxide production (VCO2), heart rate (HR), and blood pressure. Predicted values for peak VO2 and work rate were generated from predictive equations. Patients with impaired exercise capacity, defined as <80% of age-, sex- and ideal lean body mass predicted, and dyspnea on exertion underwent further exercise cardiac magnetic resonance (exCMR) imaging using an MR compatible ergometer. Biventricular volumes and contractility, RV longitudinal strain, and RV to pulmonary artery coupling were assessed at rest and with exercise. Results Baseline, clinical characteristics, and CPET data are shown in Tables 1 and 2. Forced Vital Capacity was normal without signs of airway obstruction. Three patients failed to reach their predicted physiologic limits during exercise, and CPET was terminated by the patient prematurely (e.g., muscular exertion, fatigue, & dyspnea, respectively). The mean exercise duration was 9.85 min. The mean ventilatory reserve was within normal limits (>15%) in all but 1 patient. VO2/work rate was normal with normal VO2 at the anaerobic threshold (mean 1541ml/kg/min, SD:731). Exercise capacity, as measured by peak VO2 was reduced, that is, <80% of predicted, in 5 out of the 15 patients (30%). Of these, three patients had echocardiography evidence of RV dysfunction at PE diagnosis, which had resolved at the time of CPET. There were no differences in the mean exercise time and maximal work rate achieved in those with low exercise capacity relative to normal capacity. The ventilatory equivalent for CO2 (VE/VCO2) at peak exercise was elevated (>35) in three of the five patients with decreased exercise capacity. The O2 pulse was attenuated in patients with decreased exercise capacity when compared to those with normal exercise capacity (7.5 mL.beat -1 vs. 12.9-1; p=0.037). Of the two patients who underwent exCMR; one showed reduced right ventricular ejection fraction (38%), abnormal RV strain (-11.3%), elevated right sided pressures signified by interventricular flattening upon inspiration during free breathing scan and an uncoupled RV to the pulmonary circulation. Conclusions Reduced exercise capacity is common after PE and not evident by resting evaluations. Pediatric PE patients with low exercise capacity and dyspnea seem to be characterized by either an abnormal pulmonary vascular response to exercise or decreased ventilatory efficiency. Larger studies are needed to better understand exercise pathophysiology after pediatric PE. Disclosures No relevant conflicts of interest to declare.
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Abdulbaset Alkhatib, Mohammed Aodeh, Hamza Hakmi. "STRONGLY) π- REGULAR RINGS RELATIVE TO RIGHT IDEAL): الحلقات π- المنتظمة و π- قوية الانتظام بالنسبة لمثالي يميني." Journal of natural sciences, life and applied sciences 4, no. 3 (September 27, 2020). http://dx.doi.org/10.26389/ajsrp.o250420.
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In this paper we study the notion of π- regular and strongly π- regular rings relative to right ideal. We provide several characterizations of this rings and study their properties. It is shown that every ring R is π- regular relative to any maximal right ideal of R . Also, we find necessary and sufficient conditions to be a ring R satisfies the d.c.c. on chains of the form Ra ⊇ Ra² ⊇ Λ relative to ideal for every a ∈ R . New results obtained include necessary and sufficient conditions for a ring to be π- regular, strongly π- regular and P- potent relative to right ideal.
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Quynh, Truong Cong, Adel Nailevich Abyzov, and Dao Thi Trang. "Rings all of whose finitely generated ideals are automorphism-invariant." Journal of Algebra and Its Applications, May 7, 2021, 2250159. http://dx.doi.org/10.1142/s0219498822501596.
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Rings in which each finitely generated right ideal is automorphism-invariant (right[Formula: see text]-rings) are shown to be isomorphic to a formal matrix ring. Among other results it is also shown that (i) if [Formula: see text] is a right nonsingular ring and [Formula: see text] is an integer, then [Formula: see text] is a right self injective regular ring if and only if the matrix ring [Formula: see text] is a right [Formula: see text]-ring, if and only if [Formula: see text] is a right automorphism-invariant ring and (ii) a right nonsingular ring [Formula: see text] is a right [Formula: see text]-ring if and only if [Formula: see text] is a direct sum of a square-full von Neumann regular right self-injective ring and a strongly regular ring containing all invertible elements of its right maximal ring of fractions. In particular, we show that a right semiartinian (or left semiartinian) ring [Formula: see text] is a right nonsingular right [Formula: see text]-ring if and only if [Formula: see text] is a left nonsingular left [Formula: see text]-ring.
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Alagöz, Yusuf, and Engi̇n Büyükaşık. "Max-projective modules." Journal of Algebra and Its Applications, May 7, 2020, 2150095. http://dx.doi.org/10.1142/s021949882150095x.
Full textAbstract:
Weakening the notion of [Formula: see text]-projectivity, a right [Formula: see text]-module [Formula: see text] is called max-projective provided that each homomorphism [Formula: see text], where [Formula: see text] is any maximal right ideal, factors through the canonical projection [Formula: see text]. We study and investigate properties of max-projective modules. Several classes of rings whose injective modules are [Formula: see text]-projective (respectively, max-projective) are characterized. For a commutative Noetherian ring [Formula: see text], we prove that injective modules are [Formula: see text]-projective if and only if [Formula: see text], where [Formula: see text] is [Formula: see text] and [Formula: see text] is a small ring. If [Formula: see text] is right hereditary and right Noetherian then, injective right modules are max-projective if and only if [Formula: see text], where [Formula: see text] is a semisimple Artinian and [Formula: see text] is a right small ring. If [Formula: see text] is right hereditary then, injective right modules are max-projective if and only if each injective simple right module is projective. Over a right perfect ring max-projective modules are projective. We discuss the existence of non-perfect rings whose max-projective right modules are projective.