Investigation of Bounded Modules and Some related Concepts

Abstract

The definition of a class of module as well as submodule namely (bounded module and bounded submodule) has introduced in  various ways.  In this study, we concentrate on some comparisons  and analyzations of bounded module’s properties and its relation specifically with prime module and other types of modules and submodules such as: scalar, multiplication, and cyclic modules. In addition, we scan the behavior of this concept under some conditions in order to reach other types of modules and given some counterexamples for several unsatisfying relationships. Finally, we add some new results about some types of modules that are related to bounded modules and open a new path that encourage other researchers about this topic.