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

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik -- Algebra och logik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Algebra and Logic (hsv//eng)

Nyckelord

Cayley–Dickson algebra

Cayley–Dickson construction

Cayley double

flipped non-associative Ore extensions

flipped non-associative polynomial rings

flipped non-associative skew polynomial rings

Mathematics/Applied Mathematics

matematik/tillämpad matematik

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