On Weakly Prime Submodules - Hadi, I. M.A. (Ibn AL-Haitham Journal For Pure and Applied Sciences, 2017)
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 ïƒŽ R, x ïƒŽ M, 0 ï‚¹ r x ïƒŽ N implies x ïƒŽ N or r ïƒŽ (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 ïƒŽ R, 0 ï‚¹ a b ïƒŽ P implies a ïƒŽ P or b ïƒŽ P. Various properties of weakly prime submodules are considered.