On m-Regular Rings

Abstract

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

Keywords

• m-regular rings
• -regular rings
• reduced rings
• locally rings
• uniform rings and 2-primal rings