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Displaying similar documents to “On generalized CS-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.

Relative Gorenstein injective covers with respect to a semidualizing module

Elham Tavasoli, Maryam Salimi (2017)

Czechoslovak Mathematical Journal

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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 ) ...

Derived dimension via τ -tilting theory

Yingying Zhang (2021)

Czechoslovak Mathematical Journal

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Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support τ -tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given τ -tilting module.

Relative tilting modules with respect to a semidualizing module

Maryam Salimi (2019)

Czechoslovak Mathematical Journal

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Let R be a commutative Noetherian ring, and let C be a semidualizing R -module. The notion of C -tilting R -modules is introduced as the relative setting of the notion of tilting R -modules with respect to C . Some properties of tilting and C -tilting modules and the relations between them are mentioned. It is shown that every finitely generated C -tilting R -module is C -projective. Finally, we investigate some kernel subcategories related to C -tilting modules.

Dual modules and reflexive modules with respect to a semidualizing module

Lixin Mao (2024)

Czechoslovak Mathematical Journal

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Let C be a semidualizing module over a commutative ring. We first investigate the properties of C -dual, C -torsionless and C -reflexive modules. Then we characterize some rings such as coherent rings, Π -coherent rings and FP-injectivity of C using C -dual, C -torsionless and C -reflexive properties of some special modules.

On the invariance of certain types of generalized Cohen-Macaulay modules under Foxby equivalence

Kosar Abolfath Beigi, Kamran Divaani-Aazar, Massoud Tousi (2022)

Czechoslovak Mathematical Journal

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Let R be a local ring and C a semidualizing module of R . We investigate the behavior of certain classes of generalized Cohen-Macaulay R -modules under the Foxby equivalence between the Auslander and Bass classes with respect to C . In particular, we show that generalized Cohen-Macaulay R -modules are invariant under this equivalence and if M is a finitely generated R -module in the Auslander class with respect to C such that C R M is surjective Buchsbaum, then M is also surjective Buchsbaum. ...

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.

A note on generalizations of semisimple modules

Engin Kaynar, Burcu N. Türkmen, Ergül Türkmen (2019)

Commentationes Mathematicae Universitatis Carolinae

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A left module M over an arbitrary ring is called an ℛ𝒟 -module (or an ℛ𝒮 -module) if every submodule N of M with Rad ( M ) N is a direct summand of (a supplement in, respectively) M . In this paper, we investigate the various properties of ℛ𝒟 -modules and ℛ𝒮 -modules. We prove that M is an ℛ𝒟 -module if and only if M = Rad ( M ) X , where X is semisimple. We show that a finitely generated ℛ𝒮 -module is semisimple. This gives us the characterization of semisimple rings in terms of ℛ𝒮 -modules. We completely determine the structure...

Special modules for R ( PSL ( 2 , q ) )

Liufeng Cao, Huixiang Chen (2023)

Czechoslovak Mathematical Journal

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Let R be a fusion ring and R : = R be the corresponding fusion algebra. We first show that the algebra R has only one left (right, two-sided) cell and the corresponding left (right, two-sided) cell module. Then we prove that, up to isomorphism, R admits a unique special module, which is 1-dimensional and given by the Frobenius-Perron homomorphism FPdim. Moreover, as an example, we explicitly determine the special module of the interpolated fusion algebra R ( PSL ( 2 , q ) ) : = r ( PSL ( 2 , q ) ) up to isomorphism, where r ( PSL ( 2 , q ) ) is the...

Generalized tilting modules over ring extension

Zhen Zhang (2019)

Czechoslovak Mathematical Journal

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Let Γ be a ring extension of R . We show the left Γ -module U = Γ R C with the endmorphism ring End Γ U = Δ is a generalized tilting module when R C is a generalized tilting module under some conditions.

Stratified modules over an extension algebra

Erzsébet Lukács, András Magyar (2018)

Czechoslovak Mathematical Journal

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Let A be a standard Koszul standardly stratified algebra and X an A -module. The paper investigates conditions which imply that the module Ext A * ( X ) over the Yoneda extension algebra A * is filtered by standard modules. In particular, we prove that the Yoneda extension algebra of A is also standardly stratified. This is a generalization of similar results on quasi-hereditary and on graded standardly stratified algebras.