ابوالفضل تاری زاده

Let R be a commutative ring with the unit element. It is shown that an ideal I in R is pure if and only if Ann(f ) + I = R for all f ∈ I. If J is the trace of a projective R-module M, we prove that J is generated by the “coordinates” of M and JM = M. These lead to a few new results and alternative proofs for some known results.