Related papers: Gorenstein homological modules over tensor rings

A left $R$-module $M$ is called two-degree Ding projective if there exists an exact sequence $...\longrightarrow D_{1}\longrightarrow D_{0}\longrightarrow D_{-1}\longrightarrow D_{-2}\longrightarrow...$ of Ding projective left $R$-modules…

Invariants with respect to recollements of the stable category of Gorenstein projective A-modules over an algebra A and stable equivalences are investigated. Specifically, the Gorenstein rigidity dimension is introduced. It is shown that…

We introduce Gorenstein silting modules (resp. complexes), and give the relation with the usual silting modules (resp. complexes). We show that Gorenstein silting modules are the module-theoretic counterpart of 2-term Gorenstein silting…

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…

In this paper we introduce compatible cleft extensions of abelian categories, and we prove that if $(\mathcal{B},\mathcal{A}, e,i,l)$ is a compatible cleft extension, then both the functor $l$ and the left adjoint of $i$ preserve Gorenstein…

Unlike the Gorenstein projective and injective dimensions, the majority of results on the Gorenstein flat dimension have been established only over Noetherian (or coherent) rings. Naturally, one would like to generalize these results to any…

A commutative noetherian ring with a dualizing complex is Gorenstein if and only if every acyclic complex of injective modules is totally acyclic. We extend this characterization, which is due to Iyengar and Krause, to arbitrary commutative…

Let $(R,\fm)$ be a local ring and let $C$ be a semidualizing $R$--module. In this paper, we are concerned in $C$--injective and $G_{C}$--injective dimensions of certain local cohomology modules of $R$. Firstly, the injective dimension of…

Let $\Lambda$ be a left and right noetherian ring. First, for $m,n\in\mathbb{N}\cup\{\infty\}$, we give equivalent conditions for a given $\Lambda$-module to be $n$-torsionfree and have $m$-torsionfree transpose. Using them, we investigate…

In this paper, we consider finitely generated modules over commutative Noetherian rings whose tensor products have finite projective dimension. We construct examples of modules of infinite projective dimension (and also of infinite…

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…

Let $G$ be a group and $R$ be a ring. We define the Gorenstein homological dimension of $G$ over $R$, denoted by ${\rm Ghd}_{R}G$, as the Gorenstein flat dimension of trivial $RG$-module $R$. It is proved that ${\rm Ghd}_SG \leq {\rm…

We develop a theory of G-dimension for modules over local homomorphisms which encompasses the classical theory of G-dimension for finite modules over local rings. As an application, we prove that a local ring R of characteristic p is…

Let $R$ be a commutative noetherian ring. Enochs and Huang [EH] proved that over a Gorenstein ring of Krull dimension $d$, every Gorenstein injective module admits a finite filtration of Gorenstein injective submodules. In this paper, we…

We study criteria for a ring - or more generally, for a small category - to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to…

For a regular normal element in an arbitrary ring, we study the category of its module factorizations. The cokernel functor relates module factorizations with Gorenstein projective components to Gorenstein projective modules over the…

We construct new complete cotorsion pairs in the categories of modules and chain complexes over a Gorenstein ring $R$, from the notions of Gorenstein homological dimensions, in order to obtain new Abelian model structures on both…

A main ingredient for Kustin-Miller unprojection, as developed in (S. Papadakis and M. Reid, Kustin-Miller unprojection without complexes, math.AG/0011094), is the module Hom_R(I, \om_R), where R is a local Gorenstein ring and I a…

For homomorphism K-->S of commutative rings, where K is Gorenstein and S is essentially of finite type and flat as a K-module, the property that all non-trivial fiber rings of K-->S are Gorenstein is characterized in terms of properties of…

In this paper, we study the problem when a finitely generated torsionless module is projective. Let $\Lambda$ be an Artinian local algebra with radical square zero. Then a finitely generated torsionless $\Lambda$-module $M$ is projective if…