The Waring Problem for Matrix Algebras

DOI10.1007/S11856-022-2366-7arXiv2103.10708MaRDI QIDQ6363244

Peter Šemrl, Matej Brešar

Publication date: 19 March 2021

Abstract: If a noncommutative polynomial $f$ is neither an identity nor a central polynomial of $mathcalA=M_n(C)$, then every trace zero matrix in $mathcalA$ can be written as a sum of two matrices from $f(mathcalA)-f(mathcalA)$. Moreover, "two" cannot be replaced by "one".

Mathematics Subject Classification ID

Other kinds of identities (generalized polynomial, rational, involution) (16R50) Matrix equations and identities (15A24) Trace rings and invariant theory (associative rings and algebras) (16R30) Semiprime p.i. rings, rings embeddable in matrices over commutative rings (16R20)

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