TY  - JOUR
TT  - NIL CLEAN INDEX OF RINGS
AU  - Basnet, Dhiren Kumar
AU  - Bhattacharyya, Jayanta
PY  - 2014
DA  - June
DO  - 10.24330/ieja.266244
JF  - International Electronic Journal of Algebra
JO  - IEJA
PB  - Abdullah HARMANCI
WT  - DergiPark
SN  - 1306-6048
SP  - 145
EP  - 156
VL  - 15
IS  - 15
KW  - Nil clean ring
KW  - nil clean index
KW  - abelian ring
N2  - 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.
UR  - https://doi.org/10.24330/ieja.266244
L1  - https://dergipark.org.tr/en/download/article-file/232767
ER  -