m-rnc rings

Abstract

In this article, an element w of an associative ring R is called m-regular nil clean or m-rnc if expressed as w = am + b where am is m-regular element and b is a nilpotent element. R is named m-regular nil clean ring or m-rnc ring. If all the elements of a ring R are m-rnc, some characteristics and basic properties of m-rnc rings are presented in this work.