Geodesic
Varieties of algebras that are solvable of index 2
Sbornik. Mathematics, Tome 43 (1982) no. 2, pp. 159-180 
S. V. Pchelintsev. Varieties of algebras that are solvable of index 2. Sbornik. Mathematics, Tome 43 (1982) no. 2, pp. 159-180. http://geodesic.mathdoc.fr/item/SM_1982_43_2_a1/
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     title = {Varieties of algebras that are solvable of index~2},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mathfrak M$ be one of the varieties $\operatorname{Alt}_2$, $(-1,1)_2$, $\operatorname{Malc}_2$ or $\operatorname{Jord}_2$ and let $\mathscr M$ be the set of all non-nilpotent subvarieties of $\mathfrak M$. This set is provided in a natural way with a certain topology. A characterization of $\mathfrak M$ is given in terms of the corresponding structure on $\mathscr M$. Bibliography: 12 titles.

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[6] Dorofeev G. V., “Primer razreshimogo, no ne nilytotentnogo $(-1,1)$-koltsa”, Algebra i logika, 12:2 (1973), 162–166 | MR | Zbl

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

[9] Pchelintsev S. V., “Svobodnaya $(-1,1)$-algebra s dvumya porozhdayuschimi”, Algebra i logika, 13:2 (1974), 425–449 | MR | Zbl

[10] Hentzel J. R., “The characterization of $(-l,l)$-rings”, J. Algebra, 30 (1974), 236–258 | DOI | MR | Zbl

[11] Sagle A. A., “Malcev algebras”, Trans. Amer. Math. Soc., 101:3 (1961), 426–458 | DOI | MR | Zbl

[12] Jacobson N., “Structure and representations of Jordan algebras”, Amer. Math. Soc. Colloq. Publ., 39, Providence, R. I., 1968 | MR | Zbl