Leibniz algebras, having a dense family of ideals

N.N. Semko; L.V. Skaskiv; O.A. Yarovaya

doi:10.15330/cmp.12.2.451-460

N.N. Semko University of the State Fiscal Service of Ukraine, 31 Universytetska str., 08205, Irpin, Ukraine https://orcid.org/0000-0003-0123-4872
L.V. Skaskiv University of the State Fiscal Service of Ukraine, 31 Universytetska str., 08205, Irpin, Ukraine https://orcid.org/0000-0001-9090-6700
O.A. Yarovaya University of the State Fiscal Service of Ukraine, 31 Universytetska str., 08205, Irpin, Ukraine https://orcid.org/0000-0002-0522-8368

https://doi.org/10.15330/cmp.12.2.451-460

Keywords: Leibniz algebra, Lie algebra, ideal, dense family, nilpotent Leibniz algebra

Published online: 2020-12-30

Abstract

We say that a Leibniz algebra $L$ has a dense family of ideals, if for every pair of subalgebras $A$, $B$ of $L$ such that $A\leqslant B$ and $A$ is not maximal in $B$ there exists an ideal $S$ such that $A\leqslant S\leqslant B$. We study the Leibniz algebras, having a dense family of ideals.

Leibniz algebras, having a dense family of ideals

Abstract

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