Accepted author manuscript, 277 KB, PDF document
Available under license: CC BY: Creative Commons Attribution 4.0 International License
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Modularity conditions in Leibniz algebras
AU - Paez-Guillan, Pilar
AU - Siciliano, Salvatore
AU - Towers, David
PY - 2024/2/14
Y1 - 2024/2/14
N2 - 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.
AB - 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.
U2 - 10.1142/S0219498825501919
DO - 10.1142/S0219498825501919
M3 - Journal article
JO - Journal of Algebra and Its Applications
JF - Journal of Algebra and Its Applications
SN - 0219-4988
ER -