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arXiv · 1612.08357

Weak clean index of a ring

Dhiren Kumar Basnet·Jayanta Bhattacharyya
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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 $ \chi(a)=\{e\in R\mid e^2=e\text{ and }a-e \mbox{ or } a+e \mbox{ is a unit}\}$. The weak clean index of $R$ is defined as $\sup \{|\chi(a)|: a\in R\}$ and it is denoted by $\win(R),$ where $| \chi(a)| $ denotes the cardinality of the set $\chi(a)$. In this article, we characterize rings of weak clean indices $1$, $2$ and $3$.

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Dhiren Kumar Basnet, Jayanta Bhattacharyya. 2016-12-26. Weak clean index of a ring. https://arxiv.org/abs/1612.08357

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