On m-Regular Rings

Abstract

As a generalization of regular rings, we introduce the notion, of m-regular rings, that is for all R a  , there is a fixed positive integer m such that m a is a Von-Neumann regular element. Some characterization and basic properties of these rings will be given. Also, we study the relationship between them and Von-Neumann regular rings, regular rings, reduced rings, locally rings, uniform rings and 2-primal rings.