Essentially prime modules and related modules

Abstract EN

Let R be a commutative ring with unity .

An R-module M is called prime if, ann M annR N for each nonzero submodules N of M .

In this paper we introduce and study the concept of essentially prime module as a generalization of prime module , where a unitary R-module M is said to be essentially prime if, ann M ann RN for each essential submodule N of M ( N≤ e M) .

.