Relevant bibliographies by topics / Rings and Algebras (math.RA)

Academic literature on the topic 'Rings and Algebras (math.RA)'

Author: Grafiati
Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Rings and Algebras (math.RA)"

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Guo, Junying, and Xiaojiang Guo. "Algebras of right ample semigroups." Open Mathematics 16, no. 1 (August 3, 2018): 842–61. http://dx.doi.org/10.1515/math-2018-0075.

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AbstractStrict RA semigroups are common generalizations of ample semigroups and inverse semigroups. The aim of this paper is to study algebras of strict RA semigroups. It is proved that any algebra of strict RA semigroups with finite idempotents has a generalized matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. In particular, it is proved that any algebra of finite right ample semigroups has a generalized upper triangular matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. As its application, we determine when an algebra of strict RA semigroups (right ample monoids) is semiprimitive. Moreover, we prove that an algebra of strict RA semigroups (right ample monoids) is left self-injective iff it is right self-injective, iff it is Frobenius, and iff the semigroup is a finite inverse semigroup.
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CARVALHO, PAULA A. A. B., and IAN M. MUSSON. "MONOLITHIC MODULES OVER NOETHERIAN RINGS." Glasgow Mathematical Journal 53, no. 3 (August 1, 2011): 683–92. http://dx.doi.org/10.1017/s0017089511000267.

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AbstractWe study finiteness conditions on essential extensions of simple modules over the quantum plane, the quantised Weyl algebra and Noetherian down-up algebras. The results achieved improve the ones obtained by Carvalho et al. (Carvalho et al., Injective modules over down-up algebras, Glasgow Math. J. 52A (2010), 53–59) for down-up algebras.
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COYETTE, CÉCILE. "MAL'CEV–NEUMANN RINGS AND NONCROSSED PRODUCT DIVISION ALGEBRAS." Journal of Algebra and Its Applications 11, no. 03 (May 24, 2012): 1250052. http://dx.doi.org/10.1142/s0219498811005804.

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The first section of this paper yields a sufficient condition for a Mal'cev–Neumann ring of formal series to be a noncrossed product division algebra. This result is used in Sec. 2 to give an elementary proof of the existence of noncrossed product division algebras (of degree 8 or degree p2 for p any odd prime). The arguments are based on those of Hanke in [A direct approach to noncrossed product division algebras, thesis dissertation, Postdam (2001), An explicit example of a noncrossed product division algebra, Math. Nachr.251 (2004) 51–68, A twisted Laurent series ring that is a noncrossed product, Israel. J. Math.150 (2005) 199–2003].
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MASUOKA, AKIRA, and MAKOTO YANAGAWA. "×R-BIALGEBRAS ASSOCIATED WITH ITERATIVE q-DIFFERENCE RINGS." International Journal of Mathematics 24, no. 04 (April 2013): 1350030. http://dx.doi.org/10.1142/s0129167x13500304.

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Realizing the possibility suggested by Hardouin [Iterative q-difference Galois theory, J. Reine Angew. Math.644 (2010) 101–144], we show that her own Picard–Vessiot (PV) theory for iterative q-difference rings is covered by the (consequently, more general) framework, settled by Amano and Masuoka [Picard–Vessiot extensions of artinian simple module algebras, J. Algebra285 (2005) 743–767], of artinian simple module algebras over a cocommutative pointed Hopf algebra. An essential point is to represent iterative q-difference modules over an iterative q-difference ring R, by modules over a certain cocommutative ×R-bialgebra. Recall that the notion of ×R-bialgebras was defined by Sweedler [Groups of simple algebras, Publ. Math. Inst. Hautes Études Sci.44 (1974) 79–189], as a generalization of bialgebras.
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PAN, SHENGYONG, ZHEN PENG, and JIE ZHANG. "DIFFERENTIAL GRADED ENDOMORPHISM ALGEBRAS, COHOMOLOGY RINGS AND DERIVED EQUIVALENCES." Glasgow Mathematical Journal 61, no. 03 (September 12, 2018): 557–73. http://dx.doi.org/10.1017/s0017089518000368.

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AbstractIn this paper, we will consider derived equivalences for differential graded endomorphism algebras by Keller's approaches. First, we construct derived equivalences of differential graded algebras which are endomorphism algebras of the objects from a triangle in the homotopy category of differential graded algebras. We also obtain derived equivalences of differential graded endomorphism algebras from a standard derived equivalence of finite dimensional algebras. Moreover, under some conditions, the cohomology rings of these differential graded endomorphism algebras are also derived equivalent. Then we give an affirmative answer to a problem of Dugas (A construction of derived equivalent pairs of symmetric algebras, Proc. Amer. Math. Soc. 143 (2015), 2281–2300) in some special case.
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Hermida-Alonso, José Ángel, Miguel V. Carriegos, Andrés Sáez-Schwedt, and Tomás Sánchez-Giralda. "On the regulator problem for linear systems over rings and algebras." Open Mathematics 19, no. 1 (January 1, 2021): 101–10. http://dx.doi.org/10.1515/math-2021-0002.

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Abstract The regulator problem is solvable for a linear dynamical system Σ \Sigma if and only if Σ \Sigma is both pole assignable and state estimable. In this case, Σ \Sigma is a canonical system (i.e., reachable and observable). When the ring R R is a field or a Noetherian total ring of fractions the converse is true. Commutative rings which have the property that the regulator problem is solvable for every canonical system (RP-rings) are characterized as the class of rings where every observable system is state estimable (SE-rings), and this class is shown to be equal to the class of rings where every reachable system is pole-assignable (PA-rings) and the dual of a canonical system is also canonical (DP-rings).
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Ánh, Phạm Ngọc. "Skew Polynomial Rings: the Schreier Technique." Acta Mathematica Vietnamica 47, no. 1 (January 22, 2022): 5–17. http://dx.doi.org/10.1007/s40306-021-00466-7.

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AbstractSchreier bases are introduced and used to show that skew polynomial rings are free ideal rings, i.e., rings whose one-sided ideals are free of unique rank, as well as to compute a rank of one-sided ideals together with a description of corresponding bases. The latter fact, a so-called Schreier-Lewin formula (Lewin Trans. Am. Math. Soc.145, 455–465 1969), is a basic tool determining a module type of perfect localizations which reveal a close connection between classical Leavitt algebras, skew polynomial rings, and free associative algebras.
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8

Izelgue, L., and O. Ouzzaouit. "Hilbert rings and G(oldman)-rings issued from amalgamated algebras." Journal of Algebra and Its Applications 17, no. 02 (January 23, 2018): 1850023. http://dx.doi.org/10.1142/s0219498818500238.

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Let [Formula: see text] and [Formula: see text] be two rings, [Formula: see text] an ideal of [Formula: see text] and [Formula: see text] be a ring homomorphism. The ring [Formula: see text] is called the amalgamation of [Formula: see text] with [Formula: see text] along [Formula: see text] with respect to [Formula: see text]. It was proposed by D’anna and Fontana [Amalgamated algebras along an ideal, Commutative Algebra and Applications (W. de Gruyter Publisher, Berlin, 2009), pp. 155–172], as an extension for the Nagata’s idealization, which was originally introduced in [Nagata, Local Rings (Interscience, New York, 1962)]. In this paper, we establish necessary and sufficient conditions under which [Formula: see text], and some related constructions, is either a Hilbert ring, a [Formula: see text]-domain or a [Formula: see text]-ring in the sense of Adams [Rings with a finitely generated total quotient ring, Canad. Math. Bull. 17(1) (1974)]. By the way, we investigate the transfer of the [Formula: see text]-property among pairs of domains sharing an ideal. Our results provide original illustrating examples.
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9

Su, Dong, and Shilin Yang. "Automorphism groups of representation rings of the weak Sweedler Hopf algebras." AIMS Mathematics 7, no. 2 (2022): 2318–30. http://dx.doi.org/10.3934/math.2022131.

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<abstract><p>Let $ \mathfrak{w}^{s}_{2, 2}(s = 0, 1) $ be two classes of weak Hopf algebras corresponding to the Sweedler Hopf algebra, and $ r(\mathfrak{w}^{s}_{2, 2}) $ be the representation rings of $ \mathfrak{w}^{s}_{2, 2} $. In this paper, we investigate the automorphism groups $ {{{\rm{Aut}}}}(r(\mathfrak{w}^{s}_{2, 2})) $ of $ r(\mathfrak{w}^{s}_{2, 2}) $, and discuss some properties of $ {{{\rm{Aut}}}}(r(\mathfrak{w}^{s}_{2, 2})) $. We obtain that $ {{{\rm{Aut}}}}(r(\mathfrak{w}^{0}_{2, 2})) $ is isomorphic to $ K_4 $, where $ K_4 $ is the Klein four-group. It is shown that $ {{{\rm{Aut}}}}(r(\mathfrak{w}^{1}_{2, 2})) $ is a non-commutative infinite solvable group, but it is not nilpotent. In addition, $ {{{\rm{Aut}}}}(r(\mathfrak{w}^{1}_{2, 2})) $ is isomorphic to $ (\mathbb{Z}\times \mathbb{Z}_{2})\rtimes \mathbb{Z}_{2} $, and its centre is isomorphic to $ \mathbb{Z}_{2} $.</p></abstract>
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10

Guo, Junying, and Xiaojiang Guo. "Generalized Munn rings." Open Mathematics 20, no. 1 (January 1, 2022): 1066–81. http://dx.doi.org/10.1515/math-2022-0487.

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Abstract Generalized Munn rings exist extensively in the theory of rings. The aim of this note is to answer when a generalized Munn ring is primitive (semiprimitive, semiprime and prime, respectively). Sufficient and necessary conditions are obtained for a generalized Munn ring with a regular sandwich matrix to be primitive (semiprimitive, semiprime and prime, respectively). Also, we obtain sufficient and necessary conditions for a Munn ring over principal ideal domains to be prime (semiprime, respectively). Our results can be regarded as the generalizations of the famous result in the theory of rings that for a ring R R , R R is primitive (semiprimitive and semiprime, respectively) if and only if so is M n ( R ) {M}_{n}\left(R) . As applications of our results, we consider the primeness and the primitivity of generalized matrix rings and generalized path algebras. In particular, it is proved that a path algebra is a semiprime if and only if it is semiprimitive.
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Book chapters on the topic "Rings and Algebras (math.RA)"

1

"Chapter VII Loop algebras of finite indecomposable RA loops." In Alternative Loop Rings, 173–94. Elsevier, 1996. http://dx.doi.org/10.1016/s0304-0208(96)80009-0.

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"Chapter XI Isomorphisms of loop algebras of finite RA loops." In Alternative Loop Rings, 267–88. Elsevier, 1996. http://dx.doi.org/10.1016/s0304-0208(96)80013-2.

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