Flipped non-associative polynomial rings and the Cayley–Dickson construction
Year: 2024
Type: article
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.
Source: Journal of Algebra
Authors: Masood Aryapoor, Per Bäck
Institution: Mälardalen University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,140
OpenAlex ID: W4402045749