Geodesic
Skew-symmetric identities of finitely generated alternative algebras
Algebra i logika, Tome 62 (2023) no. 3, pp. 387-399

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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. 
@article{AL_2023_62_3_a2,
     author = {I. P. Shestakov},
     title = {Skew-symmetric identities of finitely generated alternative algebras},
     journal = {Algebra i logika},
     pages = {387--399},
     publisher = {mathdoc},
     volume = {62},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2023_62_3_a2/}
}
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I. P. Shestakov. Skew-symmetric identities of finitely generated alternative algebras. Algebra i logika, Tome 62 (2023) no. 3, pp. 387-399. http://geodesic.mathdoc.fr/item/AL_2023_62_3_a2/