Semi – Bounded Modules

Let R be a commutative ring with identity, and let M 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 a 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 x ϵ M such that (sqrt )ann R M = (sqrt )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.