Semi-bounded modules

Abstract EN

Let R be a commutative ring with identity, and let be a unity R-module.

M is called a bounded R-module provided that there exists an element x ∈ M such that annR (M) = annR (x).

As generalization of this concept, a concept of semi-bounded module has been introduced as follows: M is called a semi-bounded if there exists an element √(ann R M) = √(ann R (x) ).

In this paper, some properties and characterizations of semi-bounded modules are given.

Also, various basic results about semi-bounded modules are considered.

Moreover, some relations between semi-bounded modules and other types of modules are considered.