Strongly J-Clean Rings with Involutions

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 i...

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Bibliographic Details
Main Authors Chen, Huanyin, Harmanci, Abdullah, Ozcan, A. Cigdem
Format Journal Article
LanguageEnglish
Published 02.07.2012
Subjects
Mathematics - Rings and Algebras
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Summary: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 $ae=ea$.
DOI:10.48550/arxiv.1207.0466