Leibniz algebras, having a dense family of ideals

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.