NEW TYPES OF REGULAR GAMMA MODULES

Abstract

Let $R$ be a $\mathrm{\Gamma }$-ring and $A$ be an $R_{\mathrm{\Gamma }}$-module. $A$ is called $F$-regular $R_{\mathrm{\Gamma }}$-module if every $R_{\mathrm{\Gamma }}$-submodule of $A$ is pure. The aim of this paper is to generalize results of $F$-regular $R$-modules and introduce theorems concerning $F$-regular $R_{\mathrm{\Gamma }}$-modules. We also explore the relationship between these modules and $R_{\mathrm{\Gamma }}$-submodules, which are a generalization of $F$-regular $R$-module semiprime submodule.