Cayley Polynomials
We consider a polynomial version of the Cayley numbers.
Namely, we define the ring of Cayley polynomials
in terms of generators and relations in the category of alternative
algebras.
The ring turns out to be an octonion algebra
over an ordinary polynomial ring. Also, a localization
(a ring of quotients) of the ring of Cayley polynomials gives another
description
of an octonion torus.
Finally, we find a subalgebra of a prime nondegenerate alternative
algebra
so that the subalgebra is an octonion algebra over the center.
Y. Yoshii < yoji.yoshii@ndsu.nodak.edu >