- Turkish Journal of Mathematics
- Vol: 38 Issue: 3
- Homological dimensions of complexes related to cotorsion pairs
Homological dimensions of complexes related to cotorsion pairs
Authors : Chongqing Wei, Limin Wang, Husheng Qiao
Pages : 401-418
Doi:10.3906/mat-1211-29
View : 8 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Cotorsion pairs, A dimension of complexes, B dimension of complexes