2016/12/26 by Dhiren Kumar Basnet, Basnet, Dhiren Kumar, Jayanta Bhattacharyya +1
Mathematics · #16N40 #16U99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1612.08357
openalex publication_date 2016/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 χ(a)=\e∈ R| e2=e and a-e or a+e is a unit\. The weak clean index of R is defined as sup \|χ(a)|: a∈ R\ and it is denoted by \win(R), where | χ(a)| denotes the cardinality of the set χ(a). In this article, we characterize rings of weak clean indices 1, 2 and 3.