SOME COVERS AND ENVELOPES IN THE CHAIN COMPLEX CATEGORY OF R-MODULES

We study the existence of some covers and envelopes in the chain complex category of R-modules. Let (A, B) be a cotorsion pair in R-Mod and let epsilon A stand for the class of all exact complexes with each term in A. We prove that (epsilon A, epsilon A(perpendicular to)) is a perfect cotorsion pair whenever A is closed under pure submodules, cokernels of pure monomorphisms and direct limits and so every complex has an epsilon A-cover. As an application we show that every complex of R-modules over a right coherent ring R has an exact Gorenstein flat cover. In addition, the existence of (A) over bar -covers and (B) over bar -envelopes of special complexes is considered where (A) over bar and (B) over bar denote the classes of all complexes with each term in A and B, respectively.