NIL CLEAN INDEX OF RINGS

Authors : Dhiren Kumar BASNET, Jayanta BHATTACHARYYA

Pages : 145-156

Doi:10.24330/ieja.266244

View : 15 | Download : 9

Publication Date : 2014-06-01

Article Type : Research Paper

Abstract :Motivated by the concept of clean index of rings of Lee and Zhou we introduce the concept of nil clean index of rings. For any element a of a ring R with unity, we define ηinsert ignore into journalissuearticles values(a); = {e ∈ R | e 2 = e and a−e ∈ nilinsert ignore into journalissuearticles values(R);}, where nilinsert ignore into journalissuearticles values(R); is the set of all nilpotent elements of R. Then nil clean index of R is defined by sup{ |ηinsert ignore into journalissuearticles values(a);| : a ∈ R} and it is denoted by Nininsert ignore into journalissuearticles values(R);. In this article, we characterize rings of nil clean indices 1, 2 and 3 and prove some interesting results pertaining them.
Keywords : Nil clean ring, nil clean index, abelian ring