Skew-symmetric identities of finitely generated alternative algebras. (English. Russian original) Zbl 07849283
Algebra Logic 62, No. 3, 257-265 (2023); translation from Algebra Logika 62, No. 3, 387-399 (2023).
Summary: 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 only for a series of skew-symmetric polynomials constructed by I. P. Shestakov in [Algebra and Logic, 16, No. 2, 153-166 (1977)].
MSC:
| 17-XX | Nonassociative rings and algebras |
References:
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