We introduce the concepts of generalized compatible and cocompatible bimodules in order
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …

Let R be a Gorenstein ring. We first study Gorenstein orthogonal classes and Gorenstein
cotorsion pairs of R-modules. Then, we introduce the concept of Gorenstein weak tilting R …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …

Given a non-negative integer n and a complete hereditary cotorsion triple, the notion of
subcategories in an abelian category is introduced. It is proved that a virtually Gorenstein …

In this paper, weak tilting modules are introduced and investigated. We show that all tilting
modules are weak tilting modules, but the converse is not true. We prove that a module is …

In this paper, we introduce quasi-Gorenstein projective and quasi-Gorenstein injective
modules, study some of their properties and investigate their behavior with respect to short …

In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an
R-module M, we show that M is Gorenstein injective if and only if Hom R (Ȓ, M) belongs to …

In this paper, we study the relative homological dimension based on the class of projectively
coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and …

Gorenstein homological algebra is an important area of mathematics, with applications in
commutative and noncommutative algebra, model category theory, representation theory …

By investigating the properties of some special covers and envelopes of modules, we prove
that if R is a Gorenstein ring with the injective envelope of RR flat, then a left R-module is …