Geodesic
Varieties of solvable index-two alternative algebras over a field of characteristic three
Matematičeskie zametki, Tome 66 (1999) no. 4, pp. 556-566 
S. V. Pchelintsev. Varieties of solvable index-two alternative algebras over a field of characteristic three. Matematičeskie zametki, Tome 66 (1999) no. 4, pp. 556-566. http://geodesic.mathdoc.fr/item/MZM_1999_66_4_a10/
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     title = {Varieties of solvable index-two alternative algebras over a~field of characteristic three},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The subvarieties of the variety $\mathrm{Alt}_2$ of solvable index-two alternative algebras over an arbitrary field of characteristic 3 are studied. The main types of such varieties are singled out in the language of identities, and inclusions between these types are established. The main results is the following. Theorem. {\it The topological rank of the variety $\mathrm{Alt}_2$ of solvable index-two alternative algebras over an arbitrary field of characteristic $3$ is equal to five}.

[1] Pchelintsev S. V., “Razreshimye indeksa 2 mnogoobraziya algebr”, Matem. sb., 115 (1981), 179–203 | MR | Zbl

[2] Medvedev Yu. A., “Konechnaya baziruemost mnogoobrazii s dvuchlennym tozhdestvom”, Algebra i logika, 17:6 (1978), 705–726 | MR

[3] Iltyakov A. V., “Reshetka podmnogoobrazii mnogoobraziya dvukhstupenchato razreshimykh alternativnykh algebr”, Algebra i logika, 21:2 (1982), 170–177 | MR

[4] Zhevlakov K. A., Slinko A. M., Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR | Zbl

[5] Dorofeev G. V., “Primer razreshimogo, no ne nilpotentnogo alternativnogo koltsa”, UMN, 15:3 (1960), 147–150 | MR

[6] Shestakov I. P., “Superalgebry i kontrprimery”, Sib. matem. zh., 32:6 (1991), 187–196 | MR