This article is cited in 2 papers

RESEARCH ARTICLE

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

V. A. Сhupordia^a, L. A. Kurdachenko^a, N. N. Semko<sup>b

a</sup> Oles Honchar Dnipro National University, 72 Gagarin avenue, 49010, Dnipro, Ukraine
^b University of the State Fiscal Service of Ukraine, 31 Universitetskaya str., 08205, Irpin, Ukraine

Abstract: 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.

MSC: 17A32, 17A60, 17A99

Received: 22.01.2020

Language: English

DOI: 10.12958/adm1533

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