What question did this study set out to answer?

This research aims to solve polynomial equations in split-octonions where coefficients are scalar, except for the constant term.

April 15, 2026

On polynomial equations over split-octonions: the arbitrary field case

Key Points

This research aims to solve polynomial equations in split-octonions where coefficients are scalar, except for the constant term.
Explored the structure of split-octonions under an arbitrary field
Solved various polynomial equations
Determined square and cubic roots of octonions
Successfully solved all relevant polynomial equations
Identified the square and cubic roots of octonions
Demonstrated the generalizability of the approach to arbitrary fields

Abstract

Over the split-octonion algebra defined over an arbitrary field, we solve all polynomial equations whose coefficients are scalar except for the constant term. As an application, we determine the square and cubic roots of an octonion.

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Authors

Artem Lopatin

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Communications in Mathematics

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On polynomial equations over split-octonions: the arbitrary field case

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Abstract

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