Dimension of complexes related to special Gorenstein projective precovers (III)

Abstract

We show that a commutative Noetherian ring R with finite Krull dimension is a Gorenstein ring if and only if Gppd ( X ) = Gpd ( X ) for any complex X of R-modules, where Gpd ( X ) is the Gorenstein projective dimension of X and Gppd ( X ) is the dimension of the complex X related to special Gorenstein projective precovers. In order to do this, the notion of DG-Gorenstein projective resolutions of complexes is introduced and a characterization of Gorenstein projective dimension of complexes is given via DG-Gorenstein projective resolutions.