Results 1 to 10 of about 306,524 (177)
Exact Embeddings into Artinian Rings [PDF]
Proceedings of the American Mathematical Society, 1993 The concept of exact embedding of a Noetherian ring into an Artinian ring discussed by Blair and Small is exploited to yield results on embeddings of various rings into Artinian rings. In particular we investigate Ore extensions, group graded rings, and filtered rings. Also, we prove that exact embeddability is a Morita invariant.
Beaulieu, Raymond A., Jensen, Anders
openaire +3 more sources
Artinian Subrings of a Commutative Ring [PDF]
Transactions of the American Mathematical Society, 1993 Given a commutative ring R R , we investigate the structure of the set of Artinian subrings of
William Heinzer, Robert Gilmer
exaly +2 more sources
Ring Extensions with Finitely Many Non-Artinian Intermediate Rings
Journal of Mathematics, 2020 The commutative ring extensions with exactly two non-Artinian intermediate rings are characterized. An initial step involves the description of the commutative ring extensions with only one non-Artinian intermediate ring.
Noômen Jarboui +2 more
doaj +2 more sources
A Result on Semi-Artinian Rings [PDF]
Proceedings of the Edinburgh Mathematical Society, 2003 AbstractIt was shown by Huynh and Rizvi that a ring $R$ is semisimple artinian if and only if every continuous right $R$-module is injective. However, a characterization of rings, over which every finitely generated continuous right module is injective, has been left open. In this note we give a partial solution for this question.
Dinh, Hai Quang, Smith, Patrick F.
exaly +3 more sources
PERFECTNESS OF THE ANNIHILATOR GRAPH OF ARTINIAN COMMUTATIVE RINGS [PDF]
Journal of Algebraic Systems, 2023 Let $R$ be a commutative ring and $Z(R)$ be the set of its zero-divisors.The annihilator graph of $R$, denoted by $AG(R)$ is a simple undirected graph whose vertexset is $Z(R)^*$, the set of all nonzero zero-divisors of $R$, and two distinct ...
M. Adlifard, Sh. Payrovi
doaj +1 more source
A characterization of artinian rings [PDF]
Glasgow Mathematical Journal, 1988 Throughout this paper we consider associative rings with identity and assume that all modules are unitary. As is well known, cyclic modules play an important role in ring theory. Many nice properties of rings can be characterized by their cyclic modules, even by their simple modules.
Dinh Van Huynh, Nguyen V. Dung
openaire +2 more sources
A note on comaximal ideal graph of commutative rings
AKCE International Journal of Graphs and Combinatorics, 2020 Let be a commutative ring with identity. The comaximal ideal graph of is a simple graph with its vertices are the proper ideals of R which are not contained in the Jacobson radical of , and two vertices and are adjacent if and only if .
S. Kavitha, R. Kala
doaj +1 more source
Journal of Mathematics, 2023 Let A be a class of some right R-modules that is closed under isomorphisms, and let M be a right R-module. Then M is called A-D3 if, whenever N and K are direct summands of M with M=N+K and M/K∈A, then N∩K is also a direct summand of M; M is called an A ...
Zhanmin Zhu
doaj +1 more source
On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
Mathematics, 2021 In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings.
Ángel Luis Muñoz Castañeda +2 more
doaj +1 more source
Global Dimension of Artinian Rings [PDF]
Proceedings of the American Mathematical Society, 1967 Introduction. It was shown by Auslander in [l] that in an Artinian ring P with radical A^O there exists an indecomposable left ideal I of square zero that satisfies the equality l.p.dim 1 = 1.p.dim N. Considering only the cyclic left ideals in an Artinian ring R we obtain a bound for the global dimension of P from Sup l.p.dim J (where J ranges over all
openaire +2 more sources