Gorenstein homological algebra is a kind of relative homological algebra which has been
developed to a high level since more than four decades. In this report we review the basic …

In this paper, we investigate the resolving resolution dimension with respect to the
recollements of abelian categories. Let (𝒜, ℬ, 𝒞) be a recollement of abelian categories such …

In this paper, we mainly investigate the $\mathfrak {X} $-Gorenstein projective dimension of
modules and the (left) $\mathfrak {X} $-Gorenstein global dimension of rings. Some …

In this paper we develop the homological properties of the Gorenstein $(\Le,\A) $-flat $ R $-
modules $\GF_ {(\Flat (R),\A)} $ proposed by Gillespie,\linebreak where the class …

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 …

Unless stated otherwise, throughout this paper all rings are associative with identity and all
modules are unitary modules. Let R be a ring. We denote by R-Mod (Mod-R) the category of …

This book is intended as a reference for mathematicians working with homological
dimensions in commutative algebra and as an introduction to Gorenstein dimensions for …

In this article, we investigate the change of rings theorems for the Gorenstein dimensions
over arbitrary rings. Namely, by the use of the notion of strongly Gorenstein modules, we …

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 …

We prove that if the Frobenius functor F (from the category of left R-modules to the category
of left S-modules) is faithful, then for any R-module X, the Gorenstein flat dimension of X is …