Classical 2-Absorbing Submodules of Modules over Commutative Rings

Abstract

In this article, all rings are commutative with nonzero identity. Let M be an R- module. A proper submodule N of M is called a classical prime submodule, if for each m is an element of M and elements a, b is an element of R, abm is an element of N implies that am is an element of N or bm is an element of N. We introduce the concept of classical 2- absorbing submodules as a generalization of classical prime submodules. We say that a proper submodule N of M is a classical 2-absorbing submodule if whenever a, b, c is an element of R and m is an element of M with abcm is an element of N, then abm is an element of N or acm is an element of N or bcm is an element of N.