Cotorsion Pairs of Modules from Left Adjoints

Abstract

Let R be a ring with 1 and M a right R-module. In this article, we will see that the functor F = M ⊗ _R – gives rise to a complete hereditary cotorsion pair where the left class consists of the F-acyclic objects. This cotorsion pair induces a Quillen model structure on Ch(R) which recovers the derived functors . An F-acyclic resolution is as good as a cofibrant replacement in this model structure. So in short, we formalize the fact that can be computed using F-acyclic resolutions.

ACKNOWLEDGMENT

The author would like to thank the referee for his or her comments and for pointing out the notion of a Lowenheim–Skolem class, which is a general model theoretic analog of Kaplansky class.

Notes

Communicated by D. Zacharia.