Results 1 to 10 of about 557 (139)

Commutative Noetherian local rings whose ideals are direct sums of cyclic modules [PDF]

Journal of Algebra, 2011
This paper is about to find which properties of the (sub-) category of \(R\)-modules reflect the structure of \(R\), where throughout \(R\) is a commutative ring with unit and any module is unital. For a recent work in the same direction see [\textit{R. Takahashi}, ``When is there a nontrivial extension-closed subcategory?'', J. Algebra 331, No. 1, 388-
Mahmood Behboodi, A Ghorbani, A Moradzadeh-Dehkordi   +2 more
exaly   +3 more sources

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, Ajim Uddin Ansari, Shiv Datt Kumar   +2 more
doaj   +2 more sources

Some Characterizations of w-Noetherian Rings and SM Rings [PDF]

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, Hwankoo Kim, Xiaolei Zhang, Jin Xie   +3 more
doaj   +2 more sources

Cotilting modules over commutative Noetherian rings [PDF]

Journal of Pure and Applied Algebra, 2014
18 pages; version 2: minor ...
Jan Trlifaj, Jan Šťovíček, Dolors Herbera   +2 more
exaly   +3 more sources

Big pure projective modules over commutative noetherian rings: Comparison with the completion

Forum Mathematicum
Abstract A module over a ring R is pure projective provided it is isomorphic to a direct summand of a direct sum of finitely presented modules. We develop tools for the classification of pure projective modules over commutative noetherian rings. In particular, for a fixed finitely presented module M, we consider
Pavel Příhoda, Dolors Herbera, Roger Wiegand   +2 more
exaly   +4 more sources

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, Sayed malek Javdannezhad, Sayedeh Fatemeh Mousavinasab   +2 more
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

On modules with finite Gorenstein dimension [PDF]

Journal of Mahani Mathematical Research
Since the seminal work of Auslander and Bridger, the theory of Gorenstein dimension (G-dimension) has undergone substantial development and attracted considerable attention.
Behruz Sadeqi
doaj   +1 more source