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Flipped non-associative polynomial rings and the Cayley-Dickson construction
- Source :
- J. Algebra 662 (2025), pp. 482-501
- Publication Year :
- 2024
-
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.<br />Comment: 17 pages; corrected an error; fixed some typos
- Subjects :
- Mathematics - Rings and Algebras
16W10, 17A20, 17A35, 17A70, 17A75, 17D05
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Algebra 662 (2025), pp. 482-501
- Publication Type :
- Report
- Accession number :
- edsarx.2403.03763
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2024.08.021