Weakly Classical Prime Submodules

Abstract

In this paper, 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 weakly classical prime submodules and we will show that this class of submodules enjoys many properties of weakly 2-absorbing ideals of commutative rings. A proper submodule N of M is a weakly classical prime submodule if whenever a, b is an element of R and m is an element of M with 0 not equal abm is an element of N, then am is an element of N or bm is an element of N.