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Homological Dimensions Of Complexes Related To Cotorsion Pairs, Chongqing Wei, Limin Wang, Husheng Qiao
Homological Dimensions Of Complexes Related To Cotorsion Pairs, Chongqing Wei, Limin Wang, Husheng Qiao
Turkish Journal of Mathematics
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.