Dimension of complexes related to special Gorenstein projective precovers (III) (Q6636357)

In this paper, the authors first introduce, the notion of \(DG\)-Gorenstein projective resolutions of complexes and a characterization of Gorenstein projective dimension of complexes is given via \(DG\)-Gorenstein projective resolutions. Using the above concept, the author proves 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.\N\NFor Part II see [the first author and \textit{M. Pengju}, Commun. Algebra 51, No. 3, 1308--1319 (2023; Zbl 1527.16006)].