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.