n-submodules

Abstract

. 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 / ∈ (cid:112) Ann R ( 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.