Modularity conditions in Leibniz algebras

Paez-Guillan, Pilar and Siciliano, Salvatore and Towers, David (2024) Modularity conditions in Leibniz algebras. Journal of Algebra and Its Applications. ISSN 0219-4988

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Abstract

In this paper we continue the study of the subalgebra lattice of a Leibniz algebra. In particular, we find out that solvable Leibniz algebras with an upper semi-modular lattice are either almost-abelian or have an abelian ideal spanned by the elements with square zero. We also study Leibniz algebras in which every subalgebra is a weak quasi-ideal, as well as modular symmetric Leibniz algebras.