Induced complete hereditary cotorsion pairs in D(R) with respect to Cartan-Eilenberg exact sequences

Abstract

Given a complete hereditary cotorsion pair (A,B) in ModR, we construct a complete hereditary cotorsion pair in the derived category D(R) of unbounded complexes with respect to the proper class ξ of cohomologically ghost triangles induced by the Cartan-Eilenberg exact sequences. More specifically, we prove that, each of the classes of projectively coresolved ξ-Gflat complexes PGF(ξ), ξ-Gflat complexes GF(ξ), ξ-Ginjective complexes GI(ξ), ξ-Gprojective complexes GP(ξ) (the last when R is virtually Gorenstein), forms one half of a complete hereditary cotorsion pair in D(R) with respect to ξ. Moreover, various homological dimensions offer additional way to obtain such cotorsion pairs in D(R) with respect to ξ.

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