NEARLY SEMI -2-ABSORBING SUBMODULES AND RELATED CONCEPTS

Abstract

In this article, R is commutative ring with identity and Y is a left unitary R-module.  A proper submodule L of Y is called nearly semiprime submodule if whenever rⁿy ∈ L, where r ∈ R and y ∈ Y, n ∈ Z⁺, implies that ry ∈ L + J(Y), where J(Y) is the Jacobson radical of Y.  This concept in courage us to introduce the concept nearly semi-2-absorbing submodule as a generalization of nearly semiprime submodule, where a proper submodule L of Y is called nearly semi-2-absorbing submodule of Y if whenever a²y ∈ L, where a ∈ R, y ∈ Y, implies that either ay ∈ L + J(Y) or a² ∈ [L : Y].  Many basic properties, and characterization of this concept are introduced.  On the other hand the relation of this concept with other classes of modules are studied.