2015/08/19 by Christensen, Lars Winther, Iyengar, Srikanth B.
#13C11 #13D05 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1508.04639
It is proved that a module M over a commutative noetherian ring R is injective if Exti((R/p)p,M)=0 holds for every i≥ 1 and every prime ideal p in R. This leads to the following characterization of injective modules: If F is faithfully flat, then a module M such that Hom(F,M) is injective and Exti(F,M)=0 for all i≥ 1 is injective. A limited version of this characterization is also proved for certain non-noetherian rings.