Results 11 to 20 of about 12,090 (94)

On Commutative Rings Whose Prime Ideals Are Direct Sums of Cyclics [PDF]

, 2012
In this paper we study commutative rings $R$ whose prime ideals are direct sums of cyclic modules. In the case $R$ is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it is shown that
Behboodi, Mahmood, Moradzadeh-Dehkordi, Ali   +1 more
core   +3 more sources

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

Totally acyclic complexes [PDF]

, 2016
For a given class of modules $\A$, we denote by $\widetilde{\A}$ the class of exact complexes $X$ having all cycles in $\A$, and by $dw(\A)$ the class of complexes $Y$ with all components $Y_j$ in $\A$.
Alina Iacob, Bass, Bennis, Bennis, Benson, Bravo, Christensen, Christensen, Enochs, Enochs, Enochs, Enochs, Enochs, Enochs, Estrada, Fossum, Gillespie, Holm, Huang, Iacob, Iacob, Iwanaga, Iwanaga, Iyengar, Krause, Murfet, Neeman, Sergio Estrada, Xianhui Fu, Yan, Yang, Yang   +31 more
core   +3 more sources

Local Cohomology Modules and Relative Cohen-Macaulayness

Discussiones Mathematicae - General Algebra and Applications, 2018
Let (R, 𝔪) denote a commutative Noetherian local ring and let M be a finite R-module. In this paper, we study relative Cohen-Macaulay rings with respect to a proper ideal 𝔞 of R and give some results on such rings in relation with Artinianness, Non ...
Zohouri M. Mast
doaj   +1 more source

Subrings of I-rings and S-rings

International Journal of Mathematics and Mathematical Sciences, 1997
Let R be a non-commutative associative ring with unity 1≠0, a left R-module is said to satisfy property (I) (resp. (S)) if every injective (resp. surjective) endomorphism of M is an automorphism of M.
Mamadou Sanghare
doaj   +1 more source

Gorenstein injective envelopes and covers over two sided noetherian rings [PDF]

, 2016
We prove that the class of Gorenstein injective modules is both enveloping and covering over a two sided noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat.
Iacob, Alina
core   +3 more sources

Structural theorem for gr-injective modules over gr-noetherian G-graded commutative rings and local cohomology functors

Izvestiya Instituta Matematiki i Informatiki. Udmurt. Gos. Univ., 2019
The author studies graded modules over graded commutative rings in analogy to the classical theory. He introduces and studies gr-Bass numbers for gr-noetherian modules over gr-noetherian graded rngs, and expresses them in terms of the functor \(Ext\). Further topics include radical and preradical functors, etc. The author also defines and uses abstract
openaire   +3 more sources

A prime ideal principle for two-sided ideals

, 2016
Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a "Prime Ideal Principle" that gives a uniform method of proving such facts, generalizing the Prime Ideal ...
Reyes, Manuel L.
core   +1 more source

When are the classes of Gorenstein modules (co)tilting?

Comptes Rendus. Mathématique
For the class of Gorenstein projective (resp. injective and flat) modules, we investigate and settle the questions when the middle class is tilting and the other ones are cotilting. The applications have in three directions.
Wang, Junpeng, Liu, Zhongkui, Zhao, Renyu   +2 more
doaj   +1 more source

Measuring birational derived splinters

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract This work is concerned with categorical methods for studying singularities. Our focus is on birational derived splinters, which is a notion that extends the definition of rational singularities beyond varieties over fields of characteristic zero. Particularly, we show that an invariant called ‘level’ in the associated derived category measures
Timothy De Deyn, Pat Lank, Kabeer Manali Rahul, Sridhar Venkatesh   +3 more
wiley   +1 more source