Geodesic
Binary Leibniz Algebras
Matematičeskie zametki, Tome 110 (2021) no. 3, pp. 336-344

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An algebra is called a binary Leibniz algebra if each of its two-generated subalgebras is a Leibniz algebra. In the present paper, we give a description of binary Leibniz algebras in terms of identities. As a consequence, we show that the variety of binary Leibniz algebras is not Schreier and that the freedom theorem fails to hold for this variety.
Keywords: Leibniz algebra, binary Lie algebra, polynomial identity. 
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     author = {N. A. Ismailov and A. S. Dzhumadil'daev},
     title = {Binary {Leibniz} {Algebras}},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_3_a1/}
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N. A. Ismailov; A. S. Dzhumadil'daev. Binary Leibniz Algebras. Matematičeskie zametki, Tome 110 (2021) no. 3, pp. 336-344. http://geodesic.mathdoc.fr/item/MZM_2021_110_3_a1/