Gorenstein homological dimensions are refinements of the classical homological
dimensions, and finiteness singles out modules with amenable properties reflecting those 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 basic homological algebra, the projective, injective and flat dimensions of modules play
an important and fundamental role. In this paper, the closely related Gorenstein projective …

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 …

A semi-dualizing module over a commutative noetherian ring A is a finitely generated
module C with RHomA (C, C)≃ A in the derived category D (A). We show how each such …

Enochs and Jenda gave some characterizations of Gorenstein injective and projective
complexes over n-Gorenstein rings. The aim of this article is to generalize these results and …

We introduce and investigate the notion of 𝐺𝐶-projective modules over (possibly non-
Noetherian) commutative rings, where 𝐶 is a semidualizing module. This extends Holm and …

The local structure of homomorphisms of commutative noetherian rings is investigated from
the point of view of dualizing complexes. A concept of finite Gorenstein dimension, which …

In 1966, Auslander introduced the notion of the $ G $-dimension of a finitely generated
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …

We define and study a notion of Gorenstein projective dimension for complexes of left
modules over associative rings. For complexes of finite Gorenstein projective dimension we …