On essential-prime sub-modules

Abstract

Let S be a commutative ring with identity, let A be an until (left) S-module. In this paper, we study the concepts : essential prime sub-modules as a generalization of prime sub-modules. A sub-module H of an S-module A is said to be essential-prime if whenever ri ∈ Si, a ∈ A with and rai ∈ Hi theni eitheri a ∈ Hi or ri ∈ [H : iA]. We give a number of basic properties and characterizations for this type of sub-modules.