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The nilpotency of Leibniz algebras with Engel condition. (English. Russian original) Zbl 1304.17003

Mosc. Univ. Math. Bull. 66, No. 3, 136-138 (2011); translation from Vest. Mosk. Univ. Mat. Mekh. 66, No. 3, 63-65 (2011).
Summary: It is proved that a Leibniz algebra over a field of zero characteristic with the Engel condition is nilpotent.

MSC:

17A32 Leibniz algebras
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[2] Yu. A. Bakhturin, Identical Relations in Lie Algebras (Nauka, Moscow, 1985; VNU Science Press, b.v., Utrecht, 1987). · Zbl 0571.17001
[3] E. I. Zelmanov, ”Engel Lie Algebras,” Dokl. Akad. Nauk SSSR 292(2), 265 (1987) [Sov. Math. Dokl. 35, 44 (1987)].
[4] S. P. Mishchenko and O. I. Cherevatenko, ”Necessary and Sufficient Conditions for a Variety of Leibniz Algebras to Have Polynomial Growth,” Fund. i Priklad. Natem. 12(8), 207 (2006) [J. Math. Sci. (N.Y.) 152 (2), 282 (2008)]. · Zbl 1184.17003
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