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arXiv · 1308.4105

Strong $J$-Cleanness of Formal Matrix Rings

Orhan Gurgun·Sait Halıcıoglu·Abdullah Harmanci
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Abstract

An element $a$ of a ring $R$ is called \emph{strongly $J$-clean} provided that there exists an idempotent $e\in R$ such that $a-e\in J(R)$ and $ae=ea$. A ring $R$ is \emph{strongly $J$-clean} in case every element in $R$ is strongly $J$-clean. In this paper, we investigate strong $J$-cleanness of $M_2(R;s)$ for a local ring $R$ and $s\in R$. We determine the conditions under which elements of $M_2(R;s)$ are strongly $J$-clean.

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Orhan Gurgun, Sait Halıcıoglu, Abdullah Harmanci. 2013-08-19. Strong $J$-Cleanness of Formal Matrix Rings. https://arxiv.org/abs/1308.4105

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