m-nil-clean nonderogatory matrices

2025/08/13 by Pojar, Andrada
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.10081

Abstract

We prove that if \mathbbF is a field of positive odd characteristic p, and m, and n are positive integers such that m≥2, and n≤ p, every n× n nonderogatory matrix A∈ \mathbbM_n(\mathbbF) which is sum of m idempotents and a nilpotent, has a decomposition A=E₁+E₂+…+E_m+V, such that E_i²=E_i, for every i∈ \1,…,m\, and V^{[(p-2)/(m)]+2}=0.

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