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arXiv · 2209.14725

A note on polynomial equations over algebras

Maximilian Illmer·Tim Netzer
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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.

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Maximilian Illmer, Tim Netzer. 2022-09-29. A note on polynomial equations over algebras. https://arxiv.org/abs/2209.14725

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