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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
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Ring Noetherian dan Ring Artinian [PDF]
Sainsmat, 2014 DOWNLOAD PDF Dalam tulisan ini, diperkenalkan dua klas khusus dari ring yaitu Ring Noetherian dan Ring Artinian. Berawal dari adanya suatu ring komutatif yang mempunyai suatu ideal (ideal kiri dan ideal kanan). Apabila ideal tersebut
. Fitriani
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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
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Nonessential sum graph of an Artinian ring [PDF]
Arab Journal of Mathematical Sciences, 2022 Purpose – The authors study the interdisciplinary relation between graph and algebraic structure ring defining a new graph, namely “non-essential sum graph”.
Bikash Barman, Kukil Kalpa Rajkhowa
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ON THE PROJECTIVE DIMENSION OF ARTINIAN MODULES [PDF]
Journal of Algebraic Systems, 2021 Let $(R, \mathfrak{m})$ be a Noetherian local ring and $M$, $N$ be two finitely generated $R$-modules. In this paper it is shown that $R$ is a Cohen-Macaulay ring if and only if $R$ admits a non-zero Artinian $R$-module $A$ of finite projective dimension;
Y. Irani, K. Bahmanpour, Gh. Ghasemi
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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
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Notes on reduced, artinian and multiplication modules [PDF]
Journal of Hyperstructures, 2014 Let M be a unitary module over a commutative ring R with identity. In this paper we consider the concepts of Artinian, semi-Artinian, reduced and multiplication modules . Also we call an R-module M radical, if it has no maximal submodule.
Jafar A’zami, Mahdieh Savaedi
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The Atiyah Conjecture and Artinian Rings [PDF]
Pure and Applied Mathematics Quarterly, 2012 Let G be a group such that its finite subgroups have bounded order, let d denote the lowest common multiple of the orders of the finite subgroups of G, and let K be a subfield of C that is closed under complex conjugation. Let U(G) denote the algebra of unbounded operators affiliated to the group von Neumann algebra N(G), and let D(KG,U(G)) denote the ...
Linnell, Peter A., Schick, Thomas
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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
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SOME RESULTS ON THE ARTINIAN COFINITE MODULES [PDF]
Journal of Algebraic Systems, 2023 Let $I$ be an ideal of a commutative Noetherian ring $R$ and $M$ be a non-zero Artinian $R$-module with support contained in $V(I)$. In this paper it is shown that $M$ is $I$-cofinite if and only if $Rad(I\widehat{R}^J+Ann_{\widehat{R}^J}M)=J\widehat{R ...
Gholamreza Pirmohammadi
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