Geodesic
On some Leibniz algebras having small dimension
Algebra and discrete mathematics, Tome 27 (2019) no. 2, pp. 292-308.

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The first step in the study of all types of algebras is the description of such algebras having small dimensions. The structure of 3-dimensional Leibniz algebras is more complicated than 1- and 2-dimensional cases. In this paper, we consider the structure of Leibniz algebras of dimension 3 over the finite fields. In some cases, the structure of the algebra essentially depends on the characteristic of the field, in others on the solvability of specific equations in the field, and so on.
Keywords: Leibniz algebra, ideal, factor-algebra, Leibniz kernel, finite dimensional Leibniz algebra, nilpotent Leibniz algebra, left (right) center
Mots-clés : Frattini subalgebra. 
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Viktoriia S. Yashchuk. On some Leibniz algebras having small dimension. Algebra and discrete mathematics, Tome 27 (2019) no. 2, pp. 292-308. http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a10/

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