  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.
