Journals / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2018 / Cilt: 67 - Sayı: 2
(WEAKLY) n-NIL CLEANNESS OF THE RING Zm
- Journal
- Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
- Pages
- 29–37
- DOI
- —
Abstract
Let R be an associative ring with identity. For a positive integern > 2, an element a 2 R is called n-potent if an = a . We define R to be(weakly) n-nil clean if every element in R can be written as a sum (a sumor a difference) of a nilpotent and an n-potent element in R. This concept isactually a generalization of weakly nil clean rings introduced by Danchev andMcGovern, [6]. In this paper, we completely determine all n;m 2 N such thatthe ring of integers modulo m, Zm is (weakly) n-nil clean.