Weak clean index of a ring
Abstract
Motivated by the concept of clean index of rings, we introduce the concept of weak clean index of rings. For any element a of a ring R with unity, we define (a)=\e∈ R e2=e and a-e or a+e is a unit\. The weak clean index of R is defined as \|(a)|: a∈ R\ and it is denoted by (R), where | (a)| denotes the cardinality of the set (a). In this article, we characterize rings of weak clean indices 1, 2 and 3.
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