On 2-absorbing primary submodules of modules over commutative ring with unity

In this paper, we introduce the concept of a 2-absorbing primary submodule over a commutative ring with nonzero identity which is a generalization of primary submodule. Let M be an R-module and N be a proper submodule of M. Then N is said to be a 2-absorbing primary submodule of M if whenever a, b is an element of R, m is an element of M and abm is an element of N, then am is an element of N or bm is an element of N or ab is an element of root(N : R M). We have given an example and proved number of results concerning 2-absorbing primary submodules. We have also proved the 2-absorbing primary avoidance theorem for submodules.