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International Electronic Journal of AlgebraIn this paper, we introduce and study Artinian* modules as a generalization of Artinian modules. We transfer several results of Artinian modules to Artinian* modules. We also provide several characterizations of this new class of modules. Furthermore, we investigate the existence of secondary representation for Artinian* modules over commutative ...
Hwankoo Kim, Unsal Tekir
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A generalization of Artinian modules
2022In the paper under review, the authors study a generalization of Artinian modules. Let \(R\) be a commutative ring with \(1\neq 0\) and \(M\) be a unitary \(R\)-module. As a generalization of prime ideals in module theory, a proper submodule \(N\) of \(M\) is said to be prime if for any \(r\in R\) and \(m\in M\), \( rm \in N\) implies that \( r \in ( N
HassanzadehLelekaami, Dawood +1 more
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Artinian local cohomology modules of cofinie modules
Journal of Algebra and Its Applications, 2020Let [Formula: see text] be a commutative Noetherian complete local ring and [Formula: see text] be a proper ideal of [Formula: see text]. Suppose that [Formula: see text] is a nonzero [Formula: see text]-cofinite [Formula: see text]-module of Krull dimension [Formula: see text].
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2023
Summary: In this paper we shall introduce a theory of length for Artinian modules over an arbitrary ring (with identity), assigning to each Artinian module \(A\) an ordinal number \(len(A)\) which will briefly be called the length of \(A\). We also demonstrate for some familiar properties of left Artinian ring be proved efficiently using length and ...
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Summary: In this paper we shall introduce a theory of length for Artinian modules over an arbitrary ring (with identity), assigning to each Artinian module \(A\) an ordinal number \(len(A)\) which will briefly be called the length of \(A\). We also demonstrate for some familiar properties of left Artinian ring be proved efficiently using length and ...
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The Theory of Local Homology for Artinian Modules
Southeast Asian Bulletin of Mathematics, 2000The authors develop the theory of local homology for an Artinian module \(A\) over a commutative ring \(R\) with identity with respect to the following concepts: Starting from an ideal \({\mathfrak a}\subset R\) and its \({\mathfrak a}\)-adic completion functor the authors study \({\mathfrak a}\)-cotorsion modules and \({\mathfrak a}\)-cotorsion-free ...
Dibaei, M. T., Divaani-Aazar, K.
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On the Krull―Schmidt Theorem for Artinian Modules
Journal of Mathematical Sciences, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Product closed modules need not be artinian
Publicationes Mathematicae Debrecen, 2007In the paper, the author constructs a module \(M\) with the following properties: (i) it is product closed (i.e., every hereditary pretorsion class in \(\sigma[M]\) is closed under products in \(\sigma[M]\)); (ii) \(M\) is finitely generated; (iii) \(M\) is not Artinian.
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On \(\alpha\)-almost Artinian type modules
Summary: In this article we introduce and study the concepts of \(\alpha\)-almost Artinian type and \(\alpha\)- Krull type modules. Using these concepts we extend some of the basic results of \(\alpha\)-almost Artinian and \(\alpha\)-Krull modules to \(\alpha\)-almost Artinian type and \(\alpha\)-Krull type modules.Davoudian, Maryam, Naseri, Nahid
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Minimal Flat Resolutions of Artinian Modules
Algebra Colloquium, 2005The purpose of this paper is to establish connection between the minimal flat resolutions of Artinian modules and the concept of cosequences in commutative algebra. The main result of this paper leads to a characterization of local Cohen–Macaulay rings in terms of vanishing property of the dual Bass numbers of certain Artinian modules.
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On the Artinianness of Graded Local Cohomology Modules
Algebra Colloquium, 2010Let R = ⨁n≥ 0 Rn be a homogeneous noetherian ring with local base ring [Formula: see text], and N a finitely generated graded R-module. Let [Formula: see text] be the i-th local cohomology module of N with respect to R+ := ⨁n > 0 Rn. Let t be the largest integer such that [Formula: see text] is not minimax.
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