Introduction to the First Edition

Summary

Noncommutative noetherian rings are presently the subject of very active research. Recently the theory has attracted particular interest due to its applications in related areas, especially the representation theories of groups and Lie algebras. We find the subject of noetherian rings an exciting one, for its own sake as well as for its applications, and our primary purpose in writing this volume was to attract more participants into the area.

This book is an introduction to the subject intended for anyone who is potentially interested, but primarily for students who are at the level which in the United States corresponds to having completed one year of graduate study. Since the topics included in an American first year graduate course vary considerably, and since those in analogous courses in other countries (e.g., third year undergraduate or M.Sc. courses in Britain) vary even more, we have attempted to minimize the actual prerequisites in terms of material, by reviewing some topics that many readers may already have in their repertoires. More importantly, we have concentrated on developing the basic tools of the subject, in order to familiarize the student with current methodology. Thus we focus on results which can be proved from a common point of view and steer away from miraculous arguments which can be used only once. In this spirit, our treatment is deliberately not encyclopedic, but is rather aimed at what we see as the major threads and key topics of current interest.