Homological dimensions of complexes related to cotorsion pairs

Abstract

Let (A, B) be a cotorsion pair in R -Mod. We define and study notions of A dimension and B dimension of unbounded complexes, which is given by means of dg -projective resolution and dg -injective resolution, respectively.As an application, we extend the Gorenstein flat dimension of complexes, which was defined by Iacob. Gorenstein cotorsion, FP-projective, FP-injective, Ding projective, and Ding injective dimension are also extended from modules to complexes. Moreover, we characterize Noetherian rings, von Neumann regular rings, and QF rings by the FP-projective, FP-injective, and Ding projective (injective) dimension of complexes, respectively.