Tests for injectivity of modules over commutative rings
Commutative Algebra
2016-06-16 v3
Abstract
It is proved that a module M over a commutative noetherian ring R is injective if Ext^i((R/p)_p,M)=0 holds for every i\ge 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 Ext^i(F,M)=0 for all i\ge 1 is injective. A limited version of this characterization is also proved for certain non-noetherian rings.
Cite
@article{arxiv.1508.04639,
title = {Tests for injectivity of modules over commutative rings},
author = {Lars Winther Christensen and Srikanth B. Iyengar},
journal= {arXiv preprint arXiv:1508.04639},
year = {2016}
}
Comments
Updated bibliography. Final version to appear in Collect. Math.; 8 pp