MULTIPLICATION MODULES THAT ARE FINITELY GENERATED

Let R be a commutative ring with identity and M be a unitary R-module. An R-module M is called a multiplication module if for every submodule N of M there exists an ideal I of R such that N = IM. It is shown that over a Noetherian domain R with dim(R) ≤ 1, multiplication modules are cyclic or isomorphic to an invertible ideal of R. Moreover, we give a characterization of finitely generated multiplication modules.