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Relevant bibliographies by topics / Maximal nonprincipal right ideal

Academic literature on the topic 'Maximal nonprincipal right ideal'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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Journal articles on the topic "Maximal nonprincipal right ideal"

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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