Displaying similar documents to “Loewy coincident algebra and Q F -3 associated graded algebra”

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.

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.

Some module cohomological properties of Banach algebras

Elham Ilka, Amin Mahmoodi, Abasalt Bodaghi (2020)

Mathematica Bohemica

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We find some relations between module biprojectivity and module biflatness of Banach algebras 𝒜 and ℬ and their projective tensor product 𝒜 ⊗ ^ ℬ . For some semigroups S , we study module biprojectivity and module biflatness of semigroup algebras l 1 ( S ) .

On generalized CS-modules

Qingyi Zeng (2015)

Czechoslovak Mathematical Journal

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An 𝒮 -closed submodule of a module M is a submodule N for which M / N is nonsingular. A module M is called a generalized CS-module (or briefly, GCS-module) if any 𝒮 -closed submodule N of M is a direct summand of M . Any homomorphic image of a GCS-module is also a GCS-module. Any direct sum of a singular (uniform) module and a semi-simple module is a GCS-module. All nonsingular right R -modules are projective if and only if all right R -modules are GCS-modules.

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.

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.

n - gr -coherent rings and Gorenstein graded modules

Mostafa Amini, Driss Bennis, Soumia Mamdouhi (2022)

Czechoslovak Mathematical Journal

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Let R be a graded ring and n ≥ 1 be an integer. We introduce and study the notions of Gorenstein n -FP-gr-injective and Gorenstein n -gr-flat modules by using the notion of special finitely presented graded modules. On n -gr-coherent rings, we investigate the relationships between Gorenstein n -FP-gr-injective and Gorenstein n -gr-flat modules. Among other results, we prove that any graded module in R -gr (or gr- R ) admits a Gorenstein n -FP-gr-injective (or Gorenstein n -gr-flat) cover and preenvelope,...

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.

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. ...

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 ) ...