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arXiv · 1406.1240

Very clean matrices over local rings

H. Chen·B. Ungor·S. Halicioglu
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Abstract

An element $a\in R$ is very clean provided that there exists an idempotent $e\in R$ such that $ae=ea$ and either $a-e$ or $a+e$ is invertible. A ring $R$ is very clean in case every element in $R$ is very clean. We explore the necessary and sufficient conditions under which a triangular $2\times 2$ matrix ring over local rings is very clean. The very clean $2\times 2$ matrices over commutative local rings are completely determined. Applications to matrices over power series are also obtained.

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H. Chen, B. Ungor, S. Halicioglu. 2014-06-04. Very clean matrices over local rings. https://arxiv.org/abs/1406.1240

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