Quasi-projective dimension and Gorenstein projective dimension

Abstract

Gheibi, Jorgensen and Takahashi recently introduced the quasi-projective dimension, a homological invariant that extends the classical projective dimension. In this paper, we investigate this invariant from the perspective of Gorenstein homological algebra. First, we show that the quasi-projective dimension coincides with the Gorenstein projective dimension under certain conditions. Second, we introduce and study the quasi-Gorenstein projective dimension as a Gorenstein analogue of the quasi-projective dimension.