Related papers: Invariants and Gorenstein projective modules
The Gorenstein property in local algebra admits several characterizations via its module category. The goal of this paper is to collect and generalize such characterizations to the relative setting, i.e., to Gorenstein morphisms as defined…
We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein projective, then its underlying module over the the base ring is Gorenstein projective; the converse holds if the Frobenius extension is either…
In this paper, we show that stable functors of derived equivalences preserve the isomorphism classes of versal deformation rings of finitely generated Gorenstein-projective modules over finite dimensional $k$-algebras. Then we generalize…
Let $\mathcal{A}$ be an abelian category. For a pair $(\mathcal{X},\mathcal{Y}$ of classes of objects in $\mathcal{A},$ we define the weak and the $(\mathcal{X},\mathcal{Y})$-Gorenstein relative projective objects in $\mathcal{A}$. We point…
We prove that a certain eventually homological isomorphism between module categories induces a triangle equivalence between their singularity categories, Gorenstein defect categories and the stable categories of Gorenstein projective…
We consider the equivalence from the stable module category to a subcategory $\mathcal{L}_A$ of the homotopy category constructed by Kato. This equivalence induces a correspondence between distinguished triangles in the homotopy category…
Motivated by their impact on homological algebra, the change of rings results have been the subject of several interesting works in Gorenstein homological algebra over Noetherian rings. In this paper, we investigate the change of rings…
Let $\mathcal{X}$ be a class of left $R$-modules, $\mathcal{Y}$ be a class of right $R$-modules. In this paper, we introduce and study Gorenstein $(\mathcal{X}, \mathcal{Y})$-flat modules as a common generalization of some known modules…
Leclerc recently studied certain Frobenius categories in connection with cluster algebra structures on coordinate rings of intersections of opposite Schubert cells. We show that these categories admit a description as Gorenstein projective…
In this paper we study the finiteness of global Gorenstein AC-homological dimensions for rings, and answer the questions posed by Becerril, Mendoza, P\'{e}rez and Santiago. As an application, we show that any left (or right) coherent and…
This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437--445. Namely, we define and study a particular case of Gorenstein projective modules. We investigate some change of rings results for this new kind of…
An algebra $A$ is left weakly Gorenstein if any semi-Gorenstein-projective left $A$-modules is Gorenstein-projective. The weakly Gorensteinness of two kinds of algebras are answered. Using the method of the monomorphism category, it is…
In \cite{AB}, Auslander and Bridger introduced Gorenstein projective modules and only about 40 years after their introduction a finite dimensional algebra $A$ was found in \cite{JS} where the subcategory of Gorenstein projective modules did…
We study the Gorenstein weak global dimension of associative rings and its relation to the Gorenstein global dimension. In particular, we prove the conjecture that the Gorenstein weak global dimension is a left-right symmetric invariant --…
From certain triangle functors, called non-negative functors, between the bounded derived categories of abelian categories with enough projective objects, we introduce their stable functors which are certain additive functors between the…
In Commutative Algebra structure results on minimal free resolutions of Gorenstein modules are of classical interest. We define Gorenstein modules of finite length over the weighted polynomial ring via symmetric matrices in divided powers.…
In this paper, we discuss a relationship between representation theory of graded self-injective algebras and that of algebras of finite global dimension. For a positively graded self-injective algebra $A$ such that $A_0$ has finite global…
We give new properties of algebras with finite Gorenstein dimension coinciding with the dominant dimension $\geq 2$, which are called Auslander-Gorenstein algebras in the recent work of Iyama and Solberg, see \cite{IyaSol}. In particular,…
In \cite{SSZ}, the authors proved that an Artin algebra $A$ with infinite global dimension has an indecomposable module with infinite projective and infinite injective dimension, giving a new characterisation of algebras with finite global…
Motivated by understanding the Nakayama conjecture which states that algebras of infinite dominant dimension should be self-injective, we study self-orthogonal modules with virtually Gorenstein endomorphism algebras and prove the following…