On weakly classical primary submodules

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 primary 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 either am is an element of N or b(t)m is an element of N for some t >= 1. We introduce the notion of "weakly classical primary submodules". A proper submodule N of M is a weakly classical primary 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 either am is an element of N or b(t)m is an element of N for some t >= 1.