On central characteristic ideals and quasi-Noetherian Leibniz algebras

Abstract

In this paper, we define on one hand, the notions of characteristics as well as central characteristics ideals of a given Leibniz algebra g and provide a necessary condition under which for two given subalgebras J and K of g such that, J IS a a non empty subset of K. J is a central characteristics two-sided ideal of K. On the other hand, we introduce the class of quasi-Noetherian Leibniz algebras. This generalizes both the class of Noetherian Leibniz algebras and that of quasi-Noetherian Lie algebras introduced by Falih and Stewart. We provide a necessary condition for a Leibniz algebra to be quasi-Noetherian. As in the case of Lie algebras, quasi-Noetherian Leibniz algebras are shown to be closed under quotients, but not under extensions. Finally, we leverage the maximal condition of abelian ideals to provide a characterization of Noetherian Leibniz algebras.