  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.
