NIL CLEAN INDEX OF RINGS

Year 2014, Volume: 15 Issue: 15, 145 - 156, 01.06.2014

Dhiren Kumar Basnet Jayanta Bhattacharyya

https://doi.org/10.24330/ieja.266244

Cited By: 2

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 η(a) = {e ∈ R | e
2 = e and a−e ∈ nil(R)}, where
nil(R) is the set of all nilpotent elements of R. Then nil clean index of R is
defined by sup{ |η(a)| : a ∈ R} and it is denoted by Nin(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