On almost bounded submodules

Abstract EN

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 R-module M is called an almost bounded submodule if there exists x ∈ M, x ∉N 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.

Moreover, some relations between almost bounded submodules and other types of modules are considered.