Results 1 to 10 of about 12,090 (94)
On multiplication $fs$-modules and dimension symmetry [PDF]
Journal of Mahani Mathematical Research, 2023 In this paper, we first study $fs$-modules, i.e., modules with finitely many small submodules. We show that every $fs$-module with finite hollow dimension is Noetherian.
Nasrin Shirali +2 more
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Acyclic Complexes and Graded Algebras
Mathematics, 2023 We already know that the noncommutative N-graded Noetherian algebras resemble commutative local Noetherian rings in many respects. We also know that commutative rings have the important property that every minimal acyclic complex of finitely generated ...
Chaoyuan Zhou
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Some Characterizations of w-Noetherian Rings and SM Rings
Journal of Mathematics, 2022 In this paper, we characterize w-Noetherian rings and SM rings. More precisely, in terms of the u-operation on a commutative ring R, we prove that R is w-Noetherian if and only if the direct limit of rGV-torsion-free injective R-modules is injective and ...
De Chuan Zhou +3 more
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On the properties of weak CM rings
上海师范大学学报. 自然科学版, 2022 In this paper, we mainly study the properties of weak CM rings. It is a special class of Noetherian commutative rings, including Cohen-Macaulay rings, excellent rings and generalized Cohen-Macaulay rings, which can be characterized by local cohomology ...
XUE Wensi, ZHOU Caijun
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S-Noetherian rings, modules and their generalizations [PDF]
Surveys in Mathematics and its Applications, 2023 Let R be a commutative ring with identity, M an R-module and S ⊆ R a multiplicative set. Then M is called S-finite if there exist an s ∈ S and a finitely generated submodule N of M such that sM ⊆ N.
Tushar Singh +2 more
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Homological dimension based on a class of Gorenstein flat modules
Comptes Rendus. Mathématique, 2023 In this paper, we study the relative homological dimension based on the class of projectively coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and Stovicek in [26].
Dalezios, Georgios, Emmanouil, Ioannis
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Homological invariants associated to semi-dualizing bimodules [PDF]
, 2005 Cohen-Macaulay dimension for modules over a commutative noetherian local ring has been defined by A. A. Gerko. That is a homological invariant sharing many properties with projective dimension and Gorenstein dimension.
Araya, Tokuji +2 more
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Finite injective dimension over rings with Noetherian cohomology [PDF]
, 2011 We study rings which have Noetherian cohomology under the action of a ring of cohomology operators. The main result is a criterion for a complex of modules over such a ring to have finite injective dimension.
Burke, Jesse
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Class and rank of differential modules [PDF]
, 2006 A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings.
C. Allday +21 more
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On modules with finite Gorenstein dimension [PDF]
Journal of Mahani Mathematical ResearchSince the seminal work of Auslander and Bridger, the theory of Gorenstein dimension (G-dimension) has undergone substantial development and attracted considerable attention.
Behruz Sadeqi
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