On 2-Absorbing Semiprimary Submodules

In this paper, we introduce the concept of 2-absorbing semiprimary submodules in modules over a commutative ring with nonzero identity which is a generalization of 2-absorbing primary submodule. Let N be a proper submodule of an R-module M. Then N is said to be a 2-absorbing semiprimary submodule of M if whenever a(1)a(2) is an element of R, m is an element of M and a(1)a(2)m is an element of N, then a(1)a(2) is an element of root(N :(R) M) or aim is an element of N or a(2)(n)m is an element of N, for some positive integer n. We have given an example and proved number of results concerning 2-absorbing semiprimary submodules.