Results 1 to 10 of about 12,073 (92)

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

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, Hwankoo Kim, Xiaolei Zhang, Jin Xie   +3 more
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

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  

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, Takahashi, Ryo, Yoshino, Yuji   +2 more
core   +2 more sources

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
core   +1 more source

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, D. Buchsbaum, D. Eisenbud, E.G. Evans, G. Carlsson, G. Carlsson, G. Carlsson, H. Cartan, L.L. Avramov, Luchezar L. Avramov, M. Hochster, M. Hochster, M. Hochster, P. Roberts, P. Roberts, P.M. Cohn, R. Hartshorne, Ragnar-Olaf Buchweitz, S. Halperin, Srikanth Iyengar, W. Bruns, W.G. Dwyer   +21 more
core   +3 more sources

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

Noncommutative generalizations of theorems of Cohen and Kaplansky [PDF]

, 2011
This paper investigates situations where a property of a ring can be tested on a set of "prime right ideals." Generalizing theorems of Cohen and Kaplansky, we show that every right ideal of a ring is finitely generated (resp.
A Kertész, AV Jategaonkar, AV Jategaonkar, AW Goldie, AW Goldie, BL Osofsky, BV Zabavs’kiĭ, D Eisenbud, DV Huynh, EG Evans Jr, G Krause, I Kaplansky, IS Cohen, JA Beachy, JC McConnell, JC Robson, JC Robson, JJ Koker, K Koh, K Koh, KR Goodearl, KR Goodearl, Manuel L. Reyes, ML Reyes, PF Smith, PF Smith, PF Smith, PM Cohn, R Gordon, SA Amitsur, SM Bhatwadekar, TY Lam, TY Lam, TY Lam, TY Lam, TY Lam, TY Lam, VR Chandran, VR Chandran   +38 more
core   +2 more sources