Abstract
If a noncommutative polynomial f is neither an identity nor a central polynomial of \({\cal A} = {M_n}\left(\mathbb{C} \right)\), then every trace zero matrix in \({\cal A}\) can be written as a sum of two matrices from \(f\left({\cal A} \right) - f\left({\cal A} \right)\). Moreover, “two” cannot be replaced by “one”.
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Supported by ARRS Grants P1-0288 and J1-2454.
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Brešar, M., Šemrl, P. The Waring problem for matrix algebras. Isr. J. Math. 253, 381–405 (2023). https://doi.org/10.1007/s11856-022-2366-7
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DOI: https://doi.org/10.1007/s11856-022-2366-7