An identity of degree 6 is given which is satisfied in an alternative monster and in a Skosyrskii algebra. It is proved that this identity is not a consequence of the alternativity identity, the commutativity identity, and an identity of nil-index 3. Also it is the only identity of degree at most 6, which is not a consequence of the identities mentioned. Therefore, the alternative monster and the Skosyrskii algebra are known to satisfy five independent identities.
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Translated from Algebra i Logika, Vol. 59, No. 2, pp. 215-238, March-April, 2020.
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Pchelintsev, S.V. Identities of Prime Alternative Algebras. Algebra Logic 59, 147–164 (2020). https://doi.org/10.1007/s10469-020-09587-8
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DOI: https://doi.org/10.1007/s10469-020-09587-8