Turkish Journal of Mathematics
Abstract
In this paper, we study completeness of cotorsion pairs in the category of complexes of R-modules. Let (A, B) be a cotorsion pair in R-Mod. It is shown that the cotorsion pair (\widetilde{A}, dg\widetilde{B}) and (\overline{A}, \overline{A}^{\perp}) are complete if A is closed under pure submodules and cokernels of pure monomorphisms, where in Gillespie's definitions \widetilde{A} is the class of exact complexes with cycles in A and dg\widetilde{B} is the class of complexes X with components in B such that the complex Hom(A, X) is exact for every complex A \in \widetilde{A}; and \overline{A} is the class of all complexes with components in A. Furthermore, they are perfect. As an application, we get that every complex over a right coherent ring has a Gorenstein flat cover, which generalizes the well-known results on the existence of Gorenstein flat covers.
DOI
10.3906/mat-1109-14
Keywords
Complete, cotorsion pair, cover, Gorenstein flat complex
First Page
852
Last Page
862
Recommended Citation
WANG, Z, & LIU, Z (2013). Complete cotorsion pairs in the category of complexes. Turkish Journal of Mathematics 37 (5): 852-862. https://doi.org/10.3906/mat-1109-14
