Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

Gorenstein homological dimensions are refinements of the classical homological
dimensions, and finiteness singles out modules with amenable properties reflecting those of …

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 …

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

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 …

The concept of Gorenstein dimension, defined by Auslander and Bridger for finitely
generated modules over a Noetherian ring, is studied in the context of finitely presented …

In the last years (Gorenstein) homological dimensions relative to a semidualizing module C
have been subject of several works as interesting extensions of (Gorenstein) homological …

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …

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 …

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 …