Some applications of the product of submodules in multiplication modules

Abstract

Let R be a commutative ring with identity. Let N and K be two submodules of a multiplication R-module M. ThenN=IM and K=JM for some ideals I and J of R. The product of N and K denoted by NK is defined by NK=IJM. Inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.