In this paper we construct Gorenstein-projective modules over Morita rings with zero
bimodule homomorphisms and we provide sufficient conditions for such rings to be …

Let (C, E, s) be an extriangulated category with a proper class ξ of E-triangles. We study
complete cohomology of objects in (C, E, s) by applying ξ-projective resolutions and ξ …

In this paper, we study certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a ring R yields exactly the Gorenstein projective modules. Specifically, given an exact …

We prove that any faithful Frobenius functor between abelian categories preserves the
Gorenstein projective dimension of objects. Consequently, it preserves and reflects …

We study the properties of the relative derived category DC b (A) of an abelian category A
relative to a full and additive subcategory C. In particular, when A= A-mod for a finite …

One of the open problems in Gorenstein homological algebra is: when is the class of
Gorenstein injective modules closed under arbitrary direct limits? It is known that if the class …

The aim of this paper is twofold. On one hand, we prove a slight generalization of the
stability for Gorenstein categories in [SWSW] and [Huang]; and show that the relative …

We establish a general method to construct triangle equivalences between the singularity
categories of (commutative and non-commutative) Gorenstein rings and the cluster …

Let $\A $ be an abelian category, and $\V $, $\W $ two additive full subcategories of $\A $.
We introduce and study the $\V\W $-Gorenstein subcategory of $\A $, which unifies many …