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\in M and elements a,b\in R, abm\in N implies that am\in N or bm\in 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\in R and m\in M with abcm\in N, then abm\in N or acm\in N or bcm\in N.