2014/06/30 by Lars Winther Christensen, Christensen, Lars Winther, Fatih Koksal +1
Mathematics · #13C11 #13D05 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C11 #msc:13D05
paper · pdf · doi:10.48550/arxiv.1406.7791
Minor editorial change after review. Final version, to appear in Proc. Amer. Math. Soc.; 6 pp
arxiv created 2015/04/16 · arxiv updated 2015/04/17
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 Exti(S,N)=0 for all i>0 is injective if Hom(S,N) is an injective S-module.