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

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.