Results 11 to 20 of about 12,073 (92)

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

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

Model structures on modules over Ding-Chen rings [PDF]

, 2009
An $n$-FC ring is a left and right coherent ring whose left and right self FP-injective dimension is $n$. The work of Ding and Chen in \cite{ding and chen 93} and \cite{ding and chen 96} shows that these rings possess properties which generalize those of
Gillespie, James
core   +1 more source

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

Cotorsion pairs generated by modules of bounded projective dimension

, 2007
We apply the theory of cotorsion pairs to study closure properties of classes of modules with finite projective dimension with respect to direct limit operations and to filtrations. We also prove that if the ring is an order in an $\aleph_0$-noetherian
Bazzoni, Silvana, Herbera, Dolors
core   +3 more sources

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

When do pseudo‐Gorenstein rings become Gorenstein?

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract We discuss the relationship between the trace ideal of the canonical module and pseudo‐Gorensteinness. In particular, under certain mild assumptions, we show that every positively graded domain that is both pseudo‐Gorenstein and nearly Gorenstein is Gorenstein. As an application, we clarify the relationships among nearly Gorensteinness, almost
Sora Miyashita
wiley   +1 more source

Torsion classes of extended Dynkin quivers over commutative rings

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract For a Noetherian R$R$‐algebra Λ$\Lambda$, there is a canonical inclusion torsΛ→∏p∈SpecRtors(κ(p)Λ)$\mathop {\mathsf {tors}}\Lambda \rightarrow \prod _{\mathfrak {p}\in \operatorname{Spec}R}\mathop {\mathsf {tors}}(\kappa (\mathfrak {p})\Lambda)$, and each element in the image satisfies a certain compatibility condition.
Osamu Iyama, Yuta Kimura
wiley   +1 more source