On weakly prime submodules

الملخص EN

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  R, x  M, 0  r x  N implies x  N or r  (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  R, 0  a b  P implies a  P or b  P.

Various properties of weakly prime submodules are considered.