On weakly prime submodules

Abstract

Let $ R $ be a commutative ring with non-zero identity. We define a proper submodule $ N $ of an $ R $-module $ M $ to be weakly prime if $ 0\not = rm\in N $( $ r\in R, m\in M $) implies $ m\in N $ or $ rM\subseteq N $. A number of results concerning weakly prime submodules are given. For example, we give three other characterizations of weakly prime submodules.