Cayley polynomials

We consider a polynomial version of the Cayley numbers. Namely, a ring of Cayley polynomials is defined 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 which is an octonion algebra over its center.