Geodesic
On the structure of Leibniz algebras whose subalgebras are ideals or core-free
Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 180-194

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An algebra $L$ over a field $F$ is said to be a Leibniz algebra (more precisely, a left Leibniz algebra) if it satisfies the Leibniz identity: $[[a, b], c] = [a, [b, c]] - [b, [a, c]]$ for all $a, b, c \in L$. Leibniz algebras are generalizations of Lie algebras. A subalgebra $S$ of a Leibniz algebra $L$ is called a core-free, if $S$ does not include a non-zero ideal. We study the Leibniz algebras, whose subalgebras are either ideals or core-free.
Keywords: Leibniz algebra, Lie algebra, ideal, core-free subalgebras, monolithic algebra, extraspecial algebra. 
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V. A. Сhupordia; L. A. Kurdachenko; N. N. Semko. On the structure of Leibniz algebras whose subalgebras are ideals or core-free. Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 180-194. http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a4/