Skew-symmetric identities of finitely generated alternative algebras

I. P. Shestakov<sup>ab

a</sup> Univ. of São Paulo, São Paulo, BRAZIL
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We prove that for every natural number $n$, there exists a natural number $N(n)$ such that every multilinear skew-symmetric polynomial in $N(n)$ or more variables which vanishes in the free associative algebra also vanishes in any $n$-generated alternative algebra over a field of characteristic $0$. Previously, a similar result was proved for just a series of skew-symmetric polynomials constructed by I. P. Shestakov in [Algebra and Logic, 16, No. 2, 153—166 (1977)].

Keywords: skew-symmetric identity, finitely generated alternative algebra.

UDC: 512.554.5

Received: 22.07.2022
Revised: 10.04.2024

DOI: 10.33048/alglog.2023.62.303

 English version: Algebra and Logic, 2023, 62:3, 257–265