Related papers: Gorenstein projective dimension with respect to a …

First we study the Gorenstein cohomological dimension ${\rm Gcd}_RG$ of groups $G$ over coefficient rings $R$, under changes of groups and rings; a characterization for finiteness of ${\rm Gcd}_RG$ is given. Some results in literature…

Let $R$ be a commutative Noetherian ring. In this paper, we study those finitely generated $R$-modules whose Cousin complexes provide Gorenstein injective resolutions. We call such a module a G-Gorenstein module. Characterizations of…

Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using the semidualizing modules, we define and study new classes of modules and homological dimensions and investigate the relations between them. In…

We study totally acyclic complexes of projective modules over triangular matrix rings and then use it to classify Gorenstein projective modules over such rings. We also use this classification to obtain some information concerning…

Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular. It is shown that there exists a class of modules which…

Let $A$ and $B$ be rings, $U$ a $(B, A)$-bimodule and $T=\left(\begin{smallmatrix} A & 0 \\ U & B \\\end{smallmatrix}\right)$ be the triangular matrix ring. In this paper, we characterize the Gorenstein homological dimensions of modules…

The aim of this article is to consider the spectral sequences induced by tensor-hom adjunction, and provide a number of new results. Let $R$ be a commutative Noetherian local ring of dimension $d$. In the 1st part, it is proved that $R$ is…

In this article we investigate the relations between the Gorenstein projective dimensions of $\Lambda$-modules and their socles for minimal n-Auslander-Gorenstein algebras $\Lambda$ in the sense of Iyama and Solberg \cite{IS}. First we give…

The notion of almost Gorenstein local ring introduced by V. Barucci and R. Fr\"oberg for one-dimensional Noetherian local rings which are analytically unramified has been generalized by S. Goto, N. Matsuoka and T. T. Phuong to…

Let $(R,\fm)$ be commutative Noetherian local ring. It is shown that $R$ is Cohen--Macaulay ring if there exists a Cohen--Macaulay finite (i.e. finitely generated) $R$--module with finite upper Gorenstein dimension. In addition, we show…

For a semidualizing module $C$ over a ring $R$, we study the following classes modulo exact zero divisors: $\g_C$--projectives, $\mathcal G_C$; the Auslander class $\mathcal A_C$; the Bass class $\mathcal B_C$; $\mathcal{P}_C$--projective;…

Let R be a commutative Noetherian ring. Recently, Dibaei and Sadeghi have studied the reduced grade of a horizontally linked R-module M of finite GC-dimension, where C is a semidualizing R-module. In this paper, we highly refine their…

Let $R$ be a commutative noetherian ring with a semi-dualizing module $C$. The Auslander categories with respect to $C$ are related through Foxby equivalence: $\xymatrix@C=50pt{\mathcal {A}_C(R) \ar@<0.4ex>[r]^{C\otimes^{\mathbf{L}}_{R} -}…

For a finite free EI category, we construct an explicit module over its category algebra. If in addition the category is projective over the ground field, the constructed module is Gorenstein-projective and is a maximal Cohen-Macaulay…

Let R be a semiperfect commutative Noetherian ring and C a semidualizing R-module. We study the theory of linkage for modules of finite G_C-dimension. For a horizontally linked R-module M of finite G_C-dimension, the connection of the Serre…

Let $R$ be a commutative noetherian ring. The $n$-semidualizing modules of $R$ are generalizations of its semidualizing modules. We will prove some basic properties of $n$-semidualizing modules. Our main result and example shows that the…

We study homological properties of test modules that are, in principle, modules that detect finite homological dimensions. The main outcome of our results is a generalization of a classical theorem of Auslander and Bridger: we prove that,…

For a finitely generated module $ M $ over a commutative Noetherian ring $R$, we settle the Auslander-Reiten conjecture when at least one of ${\rm Hom}_R(M,R)$ and ${\rm Hom}_R(M,M)$ has finite injective dimension. A number of new…

We prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective…

For a tensor ring $T_R(M)$, under certain conditions, we characterize the Gorenstein projective modules over $T_R(M)$, and prove that a $T_R(M)$-module $(X,u)$ is Gorenstein projective if and only if $u$ is monomorphic and ${\rm coker}(u)$…