ABSTRACT
In line with these ideas, Auslander and Bridger introduced the notion of G-dimension. It is a homological dimension for finitely generated modules over commutative noetherian rings and it gives a characterization of local Gorenstein rings, similar to the Auslander-Buchsbaum-Serre theorem. Auslander’s and Bridger’s notion of G-dimension for finitely generated modules over commutative noetherian rings is defined in terms of totally reflexive modules. Totally reflexive modules are defined by totally acyclic complexes. Gorenstein homological algebra is based on the Gorenstein injective, Gorenstein projective, and Gorenstein flat modules. The dual notion of a Gorenstein projective module is that of a Gorenstein injective module.
