Turkish Journal of Mathematics
DOI
10.3906/mat-1109-14
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.
Keywords
Complete, cotorsion pair, cover, Gorenstein flat complex
First Page
852
Last Page
862
Recommended Citation
WANG, ZHANPING and LIU, ZHONGKUI
(2013)
"Complete cotorsion pairs in the category of complexes,"
Turkish Journal of Mathematics: Vol. 37:
No.
5, Article 12.
https://doi.org/10.3906/mat-1109-14
Available at:
https://journals.tubitak.gov.tr/math/vol37/iss5/12
