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arXiv · 2403.03763

Flipped non-associative polynomial rings and the Cayley-Dickson construction

Masood Aryapoor·Per Bäck
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Abstract

We introduce and study flipped non-associative polynomial rings. In particular, we show that all Cayley-Dickson algebras naturally appear as quotients of a certain type of such rings; this extends the classical construction of the complex numbers (and quaternions) as a quotient of a (skew) polynomial ring to the octonions, and beyond. We also extend some classical results on algebraic properties of Cayley-Dickson algebras by McCrimmon to a class of flipped non-associative polynomial rings.

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Masood Aryapoor, Per Bäck. 2024-03-06. Flipped non-associative polynomial rings and the Cayley-Dickson construction. https://doi.org/10.1016/j.jalgebra.2024.08.021

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