A note on polynomial equations over algebras
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- by Maximilian Illmer and Tim Netzer
- Proc. Amer. Math. Soc. 152 (2024), 1831-1839
- DOI: https://doi.org/10.1090/proc/16630
- Published electronically: February 23, 2024
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Abstract:
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.References
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Bibliographic Information
- Maximilian Illmer
- Affiliation: Department of Mathematics, University of Innsbruck, Innrain 52, 6020 Innsbruck, Austria
- Email: maximilian.illmer@student.uibk.ac.at
- Tim Netzer
- Affiliation: Department of Mathematics, University of Innsbruck, Innrain 52, 6020 Innsbruck, Austria
- MR Author ID: 805220
- ORCID: 0000-0002-7000-6200
- Email: tim.netzer@uibk.ac.at
- Received by editor(s): November 24, 2022
- Received by editor(s) in revised form: July 12, 2023
- Published electronically: February 23, 2024
- Additional Notes: The authors did not receive support from any organization for the submitted work. The authors have no competing interests to declare that are relevant to the content of this article. Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
- Communicated by: Jerzy Weyman
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 1831-1839
- MSC (2020): Primary 16P10, 16H05, 17C60
- DOI: https://doi.org/10.1090/proc/16630
- MathSciNet review: 4728455