(WEAKLY)n NIL CLEANNESS OF THE RING Zm

Authors : A.hani KHASHAN, H.ali HANDAM

Pages : 29-37

View : 14 | Download : 8

Publication Date : 2018-08-01

Article Type : Research Paper

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 insert ignore into journalissuearticles values(weakly); n-nil clean if every element in R can be written as a sum insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(weakly); nnil clean
Keywords : Nil clean ring, n nil clean ring, weakly n nil clean ring