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SOME COVERS AND ENVELOPES IN THE CHAIN COMPLEX CATEGORY OF R-MODULES
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 90 / Issue 3 / June 2011
- Published online by Cambridge University Press:
- 31 August 2011, pp. 385-401
- Print publication:
- June 2011
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- Article
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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 ℰ𝒜 stand for the class of all exact complexes with each term in 𝒜. We prove that (ℰ𝒜,ℰ𝒜⊥) 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 ℰ𝒜-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
-covers and 
-envelopes of special complexes is considered where and denote the classes of all complexes with each term in 𝒜 and ℬ, respectively.
-covers and 
-envelopes of special complexes is considered where 