Injective Modules under Faithfully Flat Ring Extensions
Commutative Algebra
2015-04-17 v2
Abstract
Let R be a commutative ring and S be an R-algebra. It is well-known that if N is an injective R-module, then Hom(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 our main theorem that in this setting, an R-module N with Ext^i(S,N)=0 for all i>0 is injective if Hom(S,N) is an injective S-module.
Cite
@article{arxiv.1406.7791,
title = {Injective Modules under Faithfully Flat Ring Extensions},
author = {Lars Winther Christensen and Fatih Koksal},
journal= {arXiv preprint arXiv:1406.7791},
year = {2015}
}
Comments
Minor editorial change after review. Final version, to appear in Proc. Amer. Math. Soc.; 6 pp