(WEAKLY)n NIL CLEANNESS OF THE RING Zm

Abstract

Let R be an associative ring with identity. For a positive integer n > 2, an element a 2 R is called n potent if a n = a . We define R to be (weakly) n-nil clean if every element in R can be written as a sum (a sum or a difference) of a nilpotent and an npotent element in R. This concept is actually a generalization of weakly nil clean rings introduced by Danchev and McGovern, [6]. In this paper, we completely determine all n; m 2 N such that the ring of integers modulo m, Zm is (weakly) nnil clean