Speciality of Metabelian Mal''tsev Algebras
Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 257-266.

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It is proved that, for any metabelian Mal'tsev algebra $M$ over a field of characteristic $\ne2,3$, there is an alternative algebra $A$ such that the algebra $M$ can be embedded in the commutator algebra $A^{(-)}$. Moreover, the enveloping alternative algebra $A$ can be found in the variety of algebras with the identity $[x,y][z,t]=0$. The proof of this result is based on the construction of additive bases of the free metabelian Mal"tsev algebra and the free alternative algebra with the identity $[x,y][z,t] = 0$.
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S. V. Pchelintsev. Speciality of Metabelian Mal''tsev Algebras. Matematičeskie zametki, Tome 74 (2003) no. 2, pp. 257-266. http://geodesic.mathdoc.fr/item/MZM_2003_74_2_a7/

[1] Filippov V. T., “Pervichnye algebry Maltseva”, Matem. zametki, 31:5 (1982), 669–678 | MR | Zbl

[2] Sverchkov S., “Varieties of special algebras”, Comm. Algebra, 16 (1988), 1877–1919 | DOI | MR | Zbl

[3] Filippov V. T., “O vlozhenii maltsevskikh algebr v alternativnye”, Algebra i logika, 22:4 (1983), 443–465 | MR

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

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

[6] Bakhturin Yu. A., Tozhdestva v algebrakh Li, Nauka, M., 1985 | Zbl

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