Ring Theory Learning Seminar

Samuel Kim, Pure Mathematics, University of Waterloo

"Proving the Hopkins-Levitzki Theorem"

In 1939 Hopkins and Levitzki both independently proved that given a ring R with a nilpotent rad R and semisimple quotient R/ rad R that the condition of an R-module being Noetherian, Artinian, and having a composition series are equivalent. Last time Pat gave the setup for proving the Hopkins-Levitzki theorem and we were nearly there. In the next talk I briefly revisit the results from Pat’s talk then go on to the proof. In what time remains, I will also talk about some of my favourite rings and analyze their structures using The Theorem.

MC 5403