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

Abstract

Let R be a ring and X a complex of R-modules. We give some characterizations of the dimension of X related to special Gorenstein projective precovers. Let R be a ring such that forms a cotorsion pair cogenerated by a set, where denotes the category consisting of all Gorenstein projective R-modules. Then the dimension related to special Gorenstein projective precovers is equal to the infimum of the set there exists a complete Gorenstein projective resolution of X such that σi is bijective for each Forthmore, if is finite and n an integer then if and only if for any i > n and any projective R-module Q, where is the relative cohomology functor.