Geodesic
Identities of prime alternative algebras
Algebra i logika, Tome 59 (2020) no. 2, pp. 215-238.

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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.
Keywords: identity, independence of identities, alternative monster
Mots-clés : Skosyrskii algebra. 
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S. V. Pchelintsev. Identities of prime alternative algebras. Algebra i logika, Tome 59 (2020) no. 2, pp. 215-238. http://geodesic.mathdoc.fr/item/AL_2020_59_2_a3/

[1] S. V. Pchelintsev, “Izotopy alternativnogo monstra i algebry Skosyrskogo”, Sib. matem. zh., 57:4 (2016), 850–865 | MR | Zbl

[2] S. V. Pchelintsev, “O nilpotentnykh elementakh i nil-radikalakh alternativnykh algebr”, Algebra i logika, 24:6 (1985), 674–695 | MR | Zbl

[3] V. G. Skosyrskii, “Pervichnye iordanovy algebry i konstruktsiya Kantora”, Algebra i logika, 33:3 (1994), 301–316 | MR

[4] S. V. Pchelintsev, “Pervichnye alternativnye algebry, blizkie k kommutativnym”, Izv. RAN. Ser. matem., 68:1 (2004), 183–206 | MR | Zbl

[5] S. V. Pchelintsev, “Isklyuchitelnye pervichnye alternativnye algebry”, Sib. matem. zh., 48:6 (2007), 1322–1337 | MR | Zbl

[6] S. V. Pchelintsev, “Vyrozhdennye alternativnye algebry”, Sib. matem. zh., 55:2 (2014), 396–411 | MR | Zbl

[7] I. L. Kantor, “Connectionn between Poisson brackets and Jordan and Lie superalgebras”, Lie theory, differential equations and representation theory, Proc. Annu. Semin. Can. Math. Soc. (Montréal/Can., 1989), ed. V. Hussin, Centre Rech. Math. (CRM), Univ. Montréal, Montréal, 1990, 213–225 | MR

[8] S. V. Pchelintsev, “O tozhdestvakh svobodnykh konechno porozhdennykh alternativnykh algebr nad polem kharakteristiki 3”, Matem. sb., 192:9 (2001), 109–124 | MR | Zbl

[9] E. I. Zelmanov, I. P. Shestakov, “Pervichnye alternativnye superalgebry i nilpotentnost radikala svobodnoi alternativnoi algebry”, Izv. AN SSSR. Cer. matem., 54:4 (1990), 676–693 | Zbl

[10] A. N. Grishkov, I. P. Shestakov, “Commutative Moufang loops and alternative algebras”, J. Algebra, 333:1 (2011), 1–13 | MR | Zbl

[11] S. V. Pchelintsev, “Proper identities of finitely generated commutative alternative algebras”, J. Algebra, 407 (2017), 425–440 | MR

[12] S. V. Pchelintsev, “O tozhdestvakh pervichnykh alternativnykh algebr”, Mezhd. konf. "‘Maltsevskie chteniya"’ (19–23 avgusta 2019, Novosibirsk), Tez. dokl., IM SO RAN i NGU, Novosibirsk, 2019, 174 http://math.nsc.ru/conference/malmeet/19/maltsev19.pdf