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Displaying similar documents to “Structure of flat covers of injective modules”

On commutative rings whose maximal ideals are idempotent

Farid Kourki, Rachid Tribak (2019)

Commentationes Mathematicae Universitatis Carolinae

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

CF-modules over commutative rings

Ahmed Najim, Mohammed Elhassani Charkani (2018)

Commentationes Mathematicae Universitatis Carolinae

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

Some results on G C -flat dimension of modules

Ramalingam Udhayakumar, Intan Muchtadi-Alamsyah, Chelliah Selvaraj (2019)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we study some properties of G C -flat R -modules, where C is a semidualizing module over a commutative ring R and we investigate the relation between the G C -yoke with the C -yoke of a module as well as the relation between the G C -flat resolution and the flat resolution of a module over G F -closed rings. We also obtain a criterion for computing the G C -flat dimension of modules.

Characterizations of incidence modules

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

Czechoslovak Mathematical Journal

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Let R be an associative ring and M be a left R -module. We introduce the concept of the incidence module I ( X , M ) of a locally finite partially ordered set X over M . We study the properties of I ( X , M ) 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.

n -strongly Gorenstein graded modules

Zenghui Gao, Jie Peng (2019)

Czechoslovak Mathematical Journal

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Let R be a graded ring and n 1 an integer. We introduce and study n -strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that n -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be m -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever n > m . Many properties of the n -strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized....

Commutative rings whose certain modules decompose into direct sums of cyclic submodules

Farid Kourki, Rachid Tribak (2023)

Czechoslovak Mathematical Journal

Similarity:

We provide some characterizations of rings R for which every (finitely generated) module belonging to a class 𝒞 of R -modules is a direct sum of cyclic submodules. We focus on the cases, where the class 𝒞 is one of the following classes of modules: semiartinian modules, semi-V-modules, V-modules, coperfect modules and locally supplemented modules.

Artinian cofinite modules over complete Noetherian local rings

Behrouz Sadeghi, Kamal Bahmanpour, Jafar A'zami (2013)

Czechoslovak Mathematical Journal

Similarity:

Let ( R , 𝔪 ) be a complete Noetherian local ring, I an ideal of R and M a nonzero Artinian R -module. In this paper it is shown that if 𝔭 is a prime ideal of R such that dim R / 𝔭 = 1 and ( 0 : M 𝔭 ) is not finitely generated and for each i 2 the R -module Ext R i ( M , R / 𝔭 ) is of finite length, then the R -module Ext R 1 ( M , R / 𝔭 ) is not of finite length. Using this result, it is shown that for all finitely generated R -modules N with Supp ( N ) V ( I ) and for all integers i 0 , the R -modules Ext R i ( N , M ) are of finite length, if and only if, for all finitely generated R -modules...

-cofinitely supplemented modules

H. Çalışıcı, A. Pancar (2004)

Czechoslovak Mathematical Journal

Similarity:

Let R be a ring and M a right R -module. M is called -cofinitely supplemented if every submodule N of M with M N finitely generated has a supplement that is a direct summand of M . 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 R is semiperfect if and only if every free R -module is -cofinitely supplemented. In addition, if M has the...

Relative Gorenstein injective covers with respect to a semidualizing module

Elham Tavasoli, Maryam Salimi (2017)

Czechoslovak Mathematical Journal

Similarity:

Let R be a commutative Noetherian ring and let C be a semidualizing R -module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to C which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every G C -injective module G , the character module G + is G C -flat, then the class 𝒢ℐ C ( R ) 𝒜 C ( R ) is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class 𝒢ℐ C ( R ) 𝒜 C ( R ) ...