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

We introduce and study flipped non-associative polynomial rings which all Cayley-Dickson algebras naturally appear as quotients of. In particular, 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.