On finitely generated projective and flat ideals in commutative rings (Q801978)

Let R be a commutative ring with 1. The following results are proved: Theorem: A finitely generated ideal A in R is projective if and only if A is locally principal and ann(A) is generated by an idempotent. - Theorem: A finitely generated ideal A in R is flat if and only if A is locally principal and \(ann(A)=(B)\) has the property \(xB=(x)\) for all \(x\in B\). - Using these results, several known results concerning the product of projective ideals, and flat ideals are deduced. The main tool for proving the main theorems is a characterization of finitely generated projective ideals and flat ideals by means of matrices.