$n$-strongly Gorenstein graded modules

Zenghui Gao; Jie Peng

Displaying similar documents to “ $n$ -strongly Gorenstein graded 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 $n \geq 1$ 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,...

(Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras

Chao Wang, Xiao Yan Yang (2017)

Czechoslovak Mathematical Journal

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Let $Λ = (\begin{matrix} A & M \\ 0 & B \end{matrix})$ be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective $Λ$ -modules under the condition that $M$ is a cocompatible $(A, B)$ -bimodule, we establish a recollement of the stable category $\bar{Ginj (Λ)}$ . We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over $Λ$ .

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 $C \otimes_{R} M$ is surjective Buchsbaum, then $M$ is also surjective Buchsbaum. ...

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.

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.

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 structure of sequentially Cohen-Macaulay bigraded modules

Leila Parsaei Majd, Ahad Rahimi (2015)

Czechoslovak Mathematical Journal

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Let $K$ be a field and $S = K [x_{1}, ..., x_{m}, y_{1}, ..., y_{n}]$ be the standard bigraded polynomial ring over $K$ . In this paper, we explicitly describe the structure of finitely generated bigraded “sequentially Cohen-Macaulay” $S$ -modules with respect to $Q = (y_{1}, ..., y_{n})$ . Next, we give a characterization of sequentially Cohen-Macaulay modules with respect to $Q$ in terms of local cohomology modules. Cohen-Macaulay modules that are sequentially Cohen-Macaulay with respect to $Q$ are considered.

Ding projective and Ding injective modules over trivial ring extensions

Lixin Mao (2023)

Czechoslovak Mathematical Journal

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Let $R ⋉ M$ be a trivial extension of a ring $R$ by an $R$ - $R$ -bimodule $M$ such that $M_{R}$ , $_{R} M$ , ${(R, 0)}_{R ⋉ M}$ and $_{R ⋉ M} (R, 0)$ have finite flat dimensions. We prove that $(X, α)$ is a Ding projective left $R ⋉ M$ -module if and only if the sequence $M \otimes_{R} M \otimes_{R} X \overset{M \otimes α}{⟶} M \otimes_{R} X \overset{α}{\to} X$ is exact and $coker (α)$ is a Ding projective left $R$ -module. Analogously, we explicitly describe Ding injective $R ⋉ M$ -modules. As applications, we characterize Ding projective and Ding injective modules over Morita context rings with zero bimodule homomorphisms.

Weak $n$ -injective and weak $n$ -fat modules

Umamaheswaran Arunachalam, Saravanan Raja, Selvaraj Chelliah, Joseph Kennedy Annadevasahaya Mani (2022)

Czechoslovak Mathematical Journal

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We introduce and study the concepts of weak $n$ -injective and weak $n$ -flat modules in terms of super finitely presented modules whose projective dimension is at most $n$ , which generalize the $n$ -FP-injective and $n$ -flat modules. We show that the class of all weak $n$ -injective $R$ -modules is injectively resolving, whereas that of weak $n$ -flat right $R$ -modules is projectively resolving and the class of weak $n$ -injective (or weak $n$ -flat) modules together with its left (or right) orthogonal class forms...

Rings whose nonsingular right modules are $R$ -projective

Yusuf Alagöz, Sinem Benli, Engin Büyükaşık (2021)

Commentationes Mathematicae Universitatis Carolinae

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A right $R$ -module $M$ is called $R$ -projective provided that it is projective relative to the right $R$ -module $R_{R}$ . This paper deals with the rings whose all nonsingular right modules are $R$ -projective. For a right nonsingular ring $R$ , we prove that $R_{R}$ is of finite Goldie rank and all nonsingular right $R$ -modules are $R$ -projective if and only if $R$ is right finitely $Σ$ - $C S$ and flat right $R$ -modules are $R$ -projective. Then, $R$ -projectivity of the class of nonsingular injective right modules is also considered....

Homological dimensions for endomorphism algebras of Gorenstein projective modules

Aiping Zhang, Xueping Lei (2024)

Czechoslovak Mathematical Journal

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Let $A$ be a CM-finite Artin algebra with a Gorenstein-Auslander generator $E$ , $M$ be a Gorenstein projective $A$ -module and $B = {End}_{A} M$ . We give an upper bound for the finitistic dimension of $B$ in terms of homological data of $M$ . Furthermore, if $A$ is $n$ -Gorenstein for $2 \leq n < \infty$ , then we show the global dimension of $B$ is less than or equal to $n$ plus the $B$ -projective dimension of ${Hom}_{A} (M, E) .$ As an application, the global dimension of ${End}_{A} E$ is less than or equal to $n$ .

Recollements induced by good (co)silting dg-modules

Rongmin Zhu, Jiaqun Wei (2023)

Czechoslovak Mathematical Journal

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Let $U$ be a dg- $A$ -module, $B$ the endomorphism dg-algebra of $U$ . We know that if $U$ is a good silting object, then there exist a dg-algebra $C$ and a recollement among the derived categories $𝐃 (C, d)$ of $C$ , $𝐃 (B, d)$ of $B$ and $𝐃 (A, d)$ of $A$ . We investigate the condition under which the induced dg-algebra $C$ is weak nonpositive. In order to deal with both silting and cosilting dg-modules consistently, the notion of weak silting dg-modules is introduced. Thus, similar results for good cosilting dg-modules are obtained....

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.

Displaying similar documents to “ n -strongly Gorenstein graded modules”

Displaying similar documents to “ $n$ -strongly Gorenstein graded modules”