A generalization of Hopkins-levitzki theorem

Abstract

Hopkin-Levitzki theorem said that every right Artinian ring is right Noetherian. It is well-knnown that not every Artinian is Noetherian, for example the Prufer group Zp∞ is Artinian but not Noetherian. In this paper, we prove that if M is an Artinian quasi-projective finitely generated right R-module which is a self-generator, then it is Noetherian. This result can be considered as a generalization of Hopkins-Levitzki Theorem.