Relative global Gorenstein dimensions

摘要

Let ? be an abelian category. In this paper, we investigate the global (?,?)-Gorenstein projective dimension gl.GPD(?,?)(?), associated to a GP-admissible pair (?,?). We give homological conditions over (?,?) that characterize it. Moreover, given a GI-admissible pair (?,?), we study conditions under which gl.GID(?,?)(?) and gl.GPD(?,?)(?) are the same.