Multiplication and Comultiplication Modules

Let M be a faithful multiplication and comultiplication module over a commutative ring R. In this paper we investigate some results on such modules. Let R be a commutative ring with identity and M be an R-module. Then M is called a multiplication module provided for every submodule N of M there exists an ideal I of R such that N = IM. This paper is devoted to the study some of properties of prime submodules of multiplication modules.