Let R be a commutative ring and let S be an R-algebra. It is wellknown that if N is an injective R-module, then HomR(S,N) is an injective S-module. The converse is not true, not even if R is a commutative noetherian local ring and S is its completion, but it is close: It is a special case of ourmain theorem that, in this setting, an R-module N with Ext>0 R (S,N) = 0 is injective if HomR(S,N) is an injective S-module.
- Co-base change
- Faithfully flat ring extension
- Injective module