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additive decomposition 1compact objects 1exchange property 1finite fields 1idempotent complete categories 1krull-remak-schmidt-azumaya theorem 1k-th powers 1matrix theory 1triangulated categories 1waring problem 1

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math.RA2026

On the Waring Problem for Matrices over Finite Fields

Simion Breaz

The paper proves that for any finite field 𝔽_q with q ≠ 2 and any matrix size n satisfying q^n > (k‑1)^4, every n×n matrix over 𝔽_q can be written as a sum of two k‑th power matr…