Nearly 2-Absorbing Submodules And Related Concepts

Abstract

Throughout this note R is commutative ring with identity, and X be aleft unitary R-module. A proper submodule K of an R-module X is callednearly prime, if whenever implies that either( ) or [ ( ) ]. This concept us to introduce theconcept of nearly prime submodule, where a proper submodule K of anR-module X is called nearly 2-absorbing submodule, if wherever, and then either ( ) or( ) or [ ( ) ]. The aim of this paper is to study thisconcept, and gives some of its basic properties, characterization andexamples. Furthermore, we study the relation of this concept with somekind of submodules".