On Almost Bounded Submodules

Let R be a commutative ring with identity , and let M be a unitary R-module. We introduce a concept of almost bounded submodules as follows: A submodule N of an Rmodule M is called an almost bounded submodule if there exists xinM, xinN such that annR(N)=annR(x). In this paper, some properties of almost bounded submodules are given. Also, various basic results about almost bounded submodules are considered. M oreover, some relations between almost bounded submodules and other types of modules are considered.