Resumen de Tests for injectivity of modules over commutative rings

Lars Winther Christensen, Srikanth B. Iyengar

• It is proved that a module M over a commutative noetherian ring R is injective if Ext??((?/?)?,?)=0 holds for every ?⩾1 and every prime ideal ? in R. This leads to the following characterization of injective modules: If F is faithfully flat, then a module M such that Hom?(?,?) is injective and Ext??(?,?)=0 for all ?⩾1 is injective. A limited version of this characterization is also proved for certain non-noetherian rings.