Skew-symmetric identities of finitely generated alternative algebras

2022/07/04 by I. P. Shestakov, Shestakov, Ivan P.
Computer Science · Mathematics · #17D05 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2207.01195

openalex publication_date 2022/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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].

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