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arXiv · 1207.0466

Strongly J-Clean Rings with Involutions

Huanyin Chen·Abdullah Harmanci·A. Cigdem Ozcan
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Abstract

A ring with an involution * is called strongly $J$-*-clean if every element is a sum of a projection and an element of the Jacobson radical that commute. In this article, we prove several results characterizing this class of rings. It is shown that a *-ring $R$ is strongly $J$-*-clean, if and only if $R$ is uniquely clean and strongly *-clean, if and only if $R$ is uniquely strongly *-clean, that is, for any $a\in R$, there exists a unique projection $e\in R$ such that $a-e$ is invertible and $ae=ea$.

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Huanyin Chen, Abdullah Harmanci, A. Cigdem Ozcan. 2013-02-07. Strongly J-Clean Rings with Involutions. https://arxiv.org/abs/1207.0466

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