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The structure of an almost artinian module.

MATHEMATICA SCANDINAVICA, 1982
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On hypercentral groups and artinian modules

Journal of Algebra, 1976
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On Bounded Artinian-Finitary Modules

International Journal of Algebra and Computation, 2007
Let G be a group, R be a ring and A be an RG-module. We say that A is an Artinian-finitary module overRG if for every element g ∈ G, the factor-module A/CA(g) is an Artinian R-module. The study of these modules was initiated by Wehrfritz. If D is a Dedekind domain and U is an Artinian D-module, then we can associate with U some numerical invariants ...
Leonid Andreevich Kurdachenko, I Ya Subbotin   +1 more
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Artinian Local Cohomology Modules

Canadian Mathematical Bulletin, 2007
Let R be a commutative Noetherian ring, α an ideal of R and M a finitely generated R-module. Let t be a non-negative integer. It is known that if the local cohomology module is finitely generated for all i < t, then is finitely generated.
Siamak Yassemi, Parviz Sahandi
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A generalization of Artinian modules

2022
In 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, RoshanShekalgourabi, Hajar   +1 more
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Artinian local cohomology modules of cofinie modules

Journal of Algebra and Its Applications, 2020
Let [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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Equivalences Between Projective and Injective Modules and Morita Duality for Artinian Rings

Communications in Algebra, 1993
Given two rings A and R, we study the equivalences between all projective right A-modules and all injective right R-modules. We prove that such equivalences exist if and only if A and R are Artinian with a Morita duality.
COLPI, RICCARDO
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A length for Artinian modules

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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The Theory of Local Homology for Artinian Modules

Southeast Asian Bulletin of Mathematics, 2000
The 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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Product closed modules need not be artinian

Publicationes Mathematicae Debrecen, 2007
In 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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