Classical localizations of alternative algebras

Abstract

It is shown that the center of a nondegenerate, purely alter native algebra A contains a dense ideal I such that for any nonzero element t ∈I the classical localization Atof the algebra A with respect to the element t is a Cayley—Dickson algebra over its center. It is established that the classical ring of quotients of an alternative PI-algebra is a PI-algebra. The obtained results are applied to the description of von Noumann regular alternative algebras.