Back to Search
Start Over
Complete cotorsion pairs in the category of complexes
- Source :
- Volume: 37, Issue: 5 852-862, Turkish Journal of Mathematics
- Publication Year :
- 2014
- Publisher :
- TÜBİTAK, 2014.
-
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.
Details
- Language :
- Turkish
- ISSN :
- 13000098 and 13036149
- Database :
- OpenAIRE
- Journal :
- Volume: 37, Issue: 5 852-862, Turkish Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....b9812f8e8880d179f563465fbbdfe7d8