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