Open AccessNIL CLEAN INDEX OF RINGS
Author(s) -
Dhiren Kumar Basnet,
Jayanta Bhattacharyya
Publication year - 2014
Publication title -
international electronic journal of algebra
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.268
H-Index - 5
ISSN - 1306-6048
DOI - 10.24330/ieja.266244
Subject(s) - index (typography) , ring (chemistry) , nilpotent , element (criminal law) , mathematics , set (abstract data type) , discrete mathematics , combinatorics , computer science , chemistry , law , political science , world wide web , organic chemistry , programming language
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 | e2 = 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. Mathematics Subject Classification (2010): 16U99
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