Monoform Modules Relative to a Pure Property

Abstract

 The monoform concept is defined as a module in which every nonzero submodule is rational. The primary goal of this research is to study this class of modules in terms of pure property, named purely monoform modules. It constitutes an extension of the monoform modules; in fact, the monoform modules are properly included in the class of purely monoform modules. Many characteristics of a purely monoform module have been offered as analogues to those in monoform modules. A discussion of how this class of modules relates to other related modules is considered, like almost monoform, purely uniform, purely quasi-Dedekind and purely prime modules. Besides that, other characterizations of the purely monoform module have been given similar to those known and satisfied in the monoform modules.