Skew-symmetric identities of finitely generated alternative algebras

Abstract

We prove that for every natural number n there exists a natural number N(n) such that every multilinear skew-symmetric polynomial on N(n) or more variables which vanishes in the free associative algebra vanishes as well in any n-generated alternative algebra over a field of characteristic 0. Before this was proved only for a series of such polynomials constructed by the author in [7].