On the 2-absorbing Submodules

Let R be a commutative ring and M be an R-module. In this paper, we investigate some properties of 2-absorbing submodules of M. It is shown that N is a 2-absorbing submodule of M if and only if whenever IJL  N for some ideals I; J of R and a submodule L of M, then IL  N or JL  N or IJ  N :R M. Also, if N is a 2-absorbing submodule of M and M=N is Noetherian, then a chain of 2-absorbing submodules of M is constructed. Furthermore, the annihilation of E(R=p) is studied whenever 0 is a 2-absorbing submodule of E(R=p), where p is a prime ideal of R and E(R=p) is an injective envelope of R=p.