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- Title
Homological dimensions of complexes related to cotorsion pairs.
- Authors
Chongqing WEI; Limin WANG; Husheng QIAO
- 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.
- Subjects
HOMOLOGICAL algebra; DIMENSION theory (Algebra); MATHEMATICAL complexes; NOETHERIAN rings; VON Neumann regular rings; INJECTIVE functions
- Publication
Turkish Journal of Mathematics, 2014, Vol 38, Issue 3, p401
- ISSN
1300-0098
- Publication type
Article
- DOI
10.3906/mat-1211-29