A note on dg-Gorenstein injective covers

Abstract

We consider a ring R such that the class of Gorenstein injective modules is closed under direct limits. We prove that the class of dg-Gorenstein injective complexes is covering in Ch(R) if and only if every complex of Gorenstein injective modules is dg-Gorenstein injective. In particular, when R is commutative noetherian with a dualizing complex, we obtain the following result: the class of dg-Gorenstein injective complexes is covering if and only if R is Gorenstein.