Descending Chain Conditions on Leibniz Algebras

Abstract

In this work, we introduce a new class of Leibniz algebras, called quasi-Artinian Leibniz algebras, which generalizes the minimal condition on ideals. Furthermore, we provide some characterizations and give conditions under which a quasi-Artinian Leibniz algebra is Artinian. Finally, within the framework of Leibniz algebras, we establish a connection between prime ideals and the quasi-Artinian structure.