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arXiv · 2508.10081

$m$-nil-clean nonderogatory matrices

Andrada Pojar
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Abstract

We prove that if $\mathbb{F}$ is a field of positive odd characteristic $p,$ and $m,$ and $n$ are positive integers such that $m\geq2,$ and $n\leq p,$ every $n\times n$ nonderogatory matrix $A\in \mathbb{M}_n(\mathbb{F})$ which is sum of $m$ idempotents and a nilpotent, has a decomposition $A=E_1+E_2+\dots+E_m+V,$ such that $E_i^2=E_i,$ for every $i\in \{1,\dots,m\},$ and $V^{[\frac{p-2}{m}]+2}=0.$

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Andrada Pojar. 2025-08-13. $m$-nil-clean nonderogatory matrices. https://arxiv.org/abs/2508.10081

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