n-submodules

Let R be a commutative ring with identity. A proper submodule N of an R-module M is an n-submodule if rm ∈ N (r ∈ R, m ∈ M ) with r ∈/ √ AnnR(M ), then m ∈ N . A number of results concerning n-submodules are given. For example, we give other characterizations of n-submodules. Also various properties of n-submodules are considered.