Rings over which every matrix is the sum of a tripotent and a nilpotent

M Sheibani; H Chen

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arXiv · 1702.05605

Rings over which every matrix is the sum of a tripotent and a nilpotent

M Sheibani·H Chen

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Abstract

A ring $R$ is trinil clean if every element in $R$ is the sum of a tripotent and a nilpotent. If $R$ is a 2-primal strongly 2-nil-clean ring, we prove that $M_n(R)$ is trinil clean for all $n\in {\Bbb N}$. Furthermore, we show that the matrix ring over a strongly 2-nil-clean ring of bounded index is trinil clean. We thereby provide various type of rings over which every matrix is the sum of a tripotent and a nilpotent.

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M Sheibani, H Chen. 2017-02-18. Rings over which every matrix is the sum of a tripotent and a nilpotent. https://arxiv.org/abs/1702.05605

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