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## NIL CLEAN INDEX OF RINGS

#### Dhiren Kumar Basnet [1] , Jayanta Bhattacharyya [2]

##### 188 247

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.
Nil clean ring, nil clean index, abelian ring
Other ID JA58YR63SV Articles Author: Dhiren Kumar Basnet Author: Jayanta Bhattacharyya Publication Date: June 1, 2014
 Bibtex @ { ieja266244, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Abdullah HARMANCI}, year = {2014}, pages = {145 - 156}, doi = {10.24330/ieja.266244}, title = {NIL CLEAN INDEX OF RINGS}, key = {cite}, author = {Basnet, Dhiren Kumar and Bhattacharyya, Jayanta} } APA Basnet, D , Bhattacharyya, J . (2014). NIL CLEAN INDEX OF RINGS. International Electronic Journal of Algebra, 15 (15), 145-156. DOI: 10.24330/ieja.266244 MLA Basnet, D , Bhattacharyya, J . "NIL CLEAN INDEX OF RINGS". International Electronic Journal of Algebra 15 (2014): 145-156 Chicago Basnet, D , Bhattacharyya, J . "NIL CLEAN INDEX OF RINGS". International Electronic Journal of Algebra 15 (2014): 145-156 RIS TY - JOUR T1 - NIL CLEAN INDEX OF RINGS AU - Dhiren Kumar Basnet , Jayanta Bhattacharyya Y1 - 2014 PY - 2014 N1 - doi: 10.24330/ieja.266244 DO - 10.24330/ieja.266244 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 145 EP - 156 VL - 15 IS - 15 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266244 UR - https://doi.org/10.24330/ieja.266244 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra NIL CLEAN INDEX OF RINGS %A Dhiren Kumar Basnet , Jayanta Bhattacharyya %T NIL CLEAN INDEX OF RINGS %D 2014 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 15 %N 15 %R doi: 10.24330/ieja.266244 %U 10.24330/ieja.266244 ISNAD Basnet, Dhiren Kumar , Bhattacharyya, Jayanta . "NIL CLEAN INDEX OF RINGS". International Electronic Journal of Algebra 15 / 15 (June 2014): 145-156. https://doi.org/10.24330/ieja.266244 AMA Basnet D , Bhattacharyya J . NIL CLEAN INDEX OF RINGS. IEJA. 2014; 15(15): 145-156. Vancouver Basnet D , Bhattacharyya J . NIL CLEAN INDEX OF RINGS. International Electronic Journal of Algebra. 2014; 15(15): 156-145.