On the structure of Leibniz algebras, whose subalgebras are ideals or core-free

1Chupordia, VA
1Kurdachenko, LA
2Semko, NN
1Oles Honchar Dnipropetrovsk National University
2State Tax Service National University of Ukraine, Irpin
Dopov. Nac. akad. nauk Ukr. 2020, 7:17-21
Section: Mathematics
Language: English

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 subalgebra S of a Leibniz algebra L is called core-free, if S does not include the non-zero ideal. We study the Leibniz algebras, whose subalgebras are either ideals or core-free.

Keywords: core-free subalgebras, extraspecial algebra, ideal, Leibniz algebra, Lie algebra, monolithic algebra

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