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Flipped non-associative polynomial rings and the Cayley-Dickson construction
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-4471-1483
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0002-6309-8709
2025 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 662, p. 482-501Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2025. Vol. 662, p. 482-501
Keywords [en]
Cayley–Dickson algebra, Cayley–Dickson construction, Cayley double, flipped non-associative Ore extensions, flipped non-associative polynomial rings, flipped non-associative skew polynomial rings
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-66207DOI: 10.1016/j.jalgebra.2024.08.021ISI: 001312161200001Scopus ID: 2-s2.0-85203270659OAI: oai:DiVA.org:mdh-66207DiVA, id: diva2:1843328
Available from: 2024-03-08 Created: 2024-03-08 Last updated: 2024-09-26Bibliographically approved

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