Dimension of complexes related to special Gorenstein projective precovers

Abstract

Let R be a ring and X a complex of R-modules. We investigate the relationship between the dimensions and of X, where is the dimension related to special Gorenstein projective precovers, and is Gorenstein projective dimension of X. It is shown that if R is a ring such that forms a cotorsion pair cogenerated by a set, then for any bounded complex X, there is an equality We also establish the relationship between the dimensions and where is an exact sequence of complexes.