Some remarks on multiplication ideals, II

Let R be a commutative ring with identity. An module (ideal of R) A is call ed a multi plication module (ideal) if for each submodule N of A there exis ts an ideal I of R with N = IA. We give several characterizations of multip lication modules. Using the method of idealization we show how to reduce qu estions concerning multiplication modules to multiplication ideals. For exa mple, we show that if S is a commutative R-algebra and psi: M --> N an R-mo dule homomorphism where M is a multiplication R-module and N is an S-module , then S psi(M) is a multiplication S-module.