For a commutative ring R and a faithfully flat R-algebra S we prove, under mild extra assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S ⊗RM is Gorenstein flat, and that an R-module N is Gorenstein injective if and only if it is cotorsion and the left S-module HomR(S,N) is Gorenstein injective. We apply these results to the study of Gorenstein homological dimensions of unbounded complexes. In particular, we prove two theorems on stability of these dimensions under faithfully flat (co-)base change.
- Gorenstein flat dimension
- Gorenstein injective dimension
- faithfully flat base change
- faithfully flat co-base change