A note on polynomial equations over algebras

A note on polynomial equations over algebras

We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the fundamental theorem of algebra for quaternions to polynomials with two...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2024-05, Vol.152 (5), p.1831-1839
Hauptverfasser: Illmer, Maximilian, Netzer, Tim
Format: Artikel
Sprache:eng
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Research article
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Zusammenfassung:We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the fundamental theorem of algebra for quaternions to polynomials with two monomials in the leading form, while showing that it fails for three.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/16630