On Weakly Prime Submodules

Let R be a commutative ring with unity and let M be a left R-module. We define a proper submodule N of M to be a weakly prime if whenever r ϵ R, x ϵ M, 0 ≠ r x ϵ N implies x ϵ N or r ϵ (N:M ). In fact this concept is a generalization of the concept weakly prime ideal, where a proper ideal P of R is called a weakly prime, if for all a, b ϵ R, 0 ≠ a b ϵ P implies a ϵ P or b ϵ P. Various properties of weakly prime submodules are considered.