Whose all subalgebras are ideals

1Kurdachenko, LA, 2Semko, NN, 3Subbotin, IYa.
1Oles Honchar Dnipropetrovsk National University
2State Tax Service National University of Ukraine, Irpin
3National University, Los Angeles, USA
Dopov. Nac. akad. nauk Ukr. 2017, 6:9-13
Section: Mathematics
Language: Ukrainian

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 ∈ L. Leibniz algebras are generalizations of Lie algebras. A description of Leibniz algebras, whose subalgebras are ideals, is given.

Keywords: Abelian subalgebras, bilinear form, center of a Leibniz algebra, cyclic subalgebra, extraspecial subalgebra, Leibniz algebra, Lie algebra, nilpotent subalgebras
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