The search session has expired. Please query the service again.

Displaying similar documents to “Commutative rings whose certain modules decompose into direct sums of cyclic submodules”

-cofinitely supplemented modules

H. Çalışıcı, A. Pancar (2004)

Czechoslovak Mathematical Journal

Similarity:

Let be a ring and a right -module. is called -cofinitely supplemented if every submodule of with finitely generated has a supplement that is a direct summand of . In this paper various properties of the -cofinitely supplemented modules are given. It is shown that (1) Arbitrary direct sum of -cofinitely supplemented modules is -cofinitely supplemented. (2) A ring is semiperfect if and only if every free -module is -cofinitely supplemented. In addition, if has the...

On commutative rings whose maximal ideals are idempotent

Farid Kourki, Rachid Tribak (2019)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We prove that for a commutative ring , every noetherian (artinian) -module is quasi-injective if and only if every noetherian (artinian) -module is quasi-projective if and only if the class of noetherian (artinian) -modules is socle-fine if and only if the class of noetherian (artinian) -modules is radical-fine if and only if every maximal ideal of is idempotent.

Non-weight modules over the super Schrödinger algebra

Xinyue Wang, Liangyun Chen, Yao Ma (2024)

Czechoslovak Mathematical Journal

Similarity:

We construct a family of non-weight modules which are free -modules of rank 2 over the super Schrödinger algebra in -dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free -modules of rank 2 over are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.

CF-modules over commutative rings

Ahmed Najim, Mohammed Elhassani Charkani (2018)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let be a commutative ring with unit. We give some criterions for determining when a direct sum of two CF-modules over is a CF-module. When is local, we characterize the CF-modules over whose tensor product is a CF-module.

Characterizations of incidence modules

Naseer Ullah, Hailou Yao, Qianqian Yuan, Muhammad Azam (2024)

Czechoslovak Mathematical Journal

Similarity:

Let be an associative ring and be a left -module. We introduce the concept of the incidence module of a locally finite partially ordered set over . We study the properties of and give the necessary and sufficient conditions for the incidence module to be an IN-module, -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of -modules is closed under direct product and upper triangular matrix modules.

Gorenstein star modules and Gorenstein tilting modules

Peiyu Zhang (2021)

Czechoslovak Mathematical Journal

Similarity:

We introduce the notion of Gorenstein star modules and obtain some properties and a characterization of them. We mainly give the relationship between -Gorenstein star modules and -Gorenstein tilting modules, see L. Yan, W. Li, B. Ouyang (2016), and a new characterization of -Gorenstein tilting modules.

Some results on the cofiniteness of local cohomology modules

Sohrab Sohrabi Laleh, Mir Yousef Sadeghi, Mahdi Hanifi Mostaghim (2012)

Czechoslovak Mathematical Journal

Similarity:

Let be a commutative Noetherian ring, an ideal of , an -module and a non-negative integer. In this paper we show that the class of minimax modules includes the class of modules. The main result is that if the -module is finite (finitely generated), is -cofinite for all and is minimax then is -cofinite. As a consequence we show that if and are finite -modules and is minimax for all then the set of associated prime ideals of the generalized local cohomology...

Top-stable and layer-stable degenerations and hom-order

S. O. Smalø, A. Valenta (2007)

Colloquium Mathematicae

Similarity:

Using geometrical methods, Huisgen-Zimmermann showed that if M is a module with simple top, then M has no proper degeneration such that for all t. Given a module M with square-free top and a projective cover P, she showed that if and only if M has no proper degeneration where M/M ≃ N/N. We prove here these results in a more general form, for hom-order instead of degeneration-order, and we prove them algebraically. The results of Huisgen-Zimmermann follow as consequences from...