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Communications in Algebra, 2012
Let R be a commutative ring with identity. R is a finite factorization ring (FFR) if every nonzero nonunit of R has only a finite number of factorizations up to order and associates. In this article, we give a characterization of R for R[X] and R[[X]] to be an FFR.
Murat Alan
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Let R be a commutative ring with identity. R is a finite factorization ring (FFR) if every nonzero nonunit of R has only a finite number of factorizations up to order and associates. In this article, we give a characterization of R for R[X] and R[[X]] to be an FFR.
Murat Alan
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Canadian Journal of Mathematics, 1970 Throughout this paper a ring will always be an associative, not necessarily commutative ring with an identity. It is tacitly assumed that the identity of a subring coincides with that of the whole ring. A ring R is said to be residually finite if it satisfies one of the following equivalent conditions:(1) Every non-zero ideal of R is of finite index in
Chew, Kim Lin, Lawn, Sherry
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Canadian Mathematical Bulletin, 1976 This paper determines the structure of finite rings whose two sided ideals are principal as left ideals, and as right ideals. Such rings will be called principal ideal rings. Although finite rings have been studied extensively [1], [5], [12], [14] and the tools necessary for describing finite principal ideal rings have been available for thirty years ...
James L. Fisher
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Algebra and Logic, 2023
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Algebras and Representation Theory, 2005
An algebra is representation finite if there are only finitely many isomorphism classes of indecomposable \(A\)-modules. If \(R\) is a left Noetherian ring then the author calls an \(R\)-module a lattice if its socle is \(0\). In the classical case this coincides with the usual concept of lattices over classical orders.
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An algebra is representation finite if there are only finitely many isomorphism classes of indecomposable \(A\)-modules. If \(R\) is a left Noetherian ring then the author calls an \(R\)-module a lattice if its socle is \(0\). In the classical case this coincides with the usual concept of lattices over classical orders.
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On schur rings of group rings of finite groups
Communications in Algebra, 1992Schur rings are rings associated to certain partitions of finite groups. They were introduced for applications in representation theory, cfr. [3][4]. The algebric structure of these rings has not been studied in depth. In this paper we determine explicit structure constants for Schur rings, we derive conditions for separability and we compute the ...
Apostolopoulou, C. +2 more
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Finite Commutative Rings and Their Applications
2002Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject.
Bini, G, FLAMINI, FLAMINIO
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Mathematical Journal of Okayama University, 1993
A ring \(R\) is called right (left) residually finite if every right (resp. left) ideal \(I\neq (0)\) is of finite index in \(R\). The number \(N(I)\) of elements in \(R/I\) is called the norm of \(I\). The author shows that a right residually finite ring is a right fully bounded Noetherian ring and gives some characterizations of such a ring ...
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A ring \(R\) is called right (left) residually finite if every right (resp. left) ideal \(I\neq (0)\) is of finite index in \(R\). The number \(N(I)\) of elements in \(R/I\) is called the norm of \(I\). The author shows that a right residually finite ring is a right fully bounded Noetherian ring and gives some characterizations of such a ring ...
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SEMIMAXIMAL RINGS OF FINITE TYPE
Mathematics of the USSR-Sbornik, 1977Necessary and sufficient conditions are given for a semimaximal ring to have finitely many indecomposable nonisomorphic finitely generated modules that are torsion-free in the sense of Bass.Bibliography: 13 titles.
Zavadskij, A. G., Kirichenko, V. V.
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On \(S\)-finite conductor rings
2023Summary: Let \(R\) be a commutative ring with nonzero identity and \(S \subseteq R\) be a multiplicatively closed subset of \(R\). In this paper, we introduce and study \(S\)-finite conductor rings. \(R\) is said to be an \(S\)-finite conductor ring if \((0:a)\) and \(Ra\cap Rb\) are \(S\)-finite ideals of \(R\) for each \(a,b\in R\).
Anebri, Adam +2 more
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