# A First Course in Noncommutative Rings

• T. Y. Lam
Book

Part of the Graduate Texts in Mathematics book series (GTM, volume 131)

1. Front Matter
Pages i-xv
2. T. Y. Lam
Pages 1-50
3. T. Y. Lam
Pages 51-105
4. T. Y. Lam
Pages 107-162
5. T. Y. Lam
Pages 163-212
6. T. Y. Lam
Pages 213-274
7. T. Y. Lam
Pages 275-292
8. T. Y. Lam
Pages 293-343
9. T. Y. Lam
Pages 345-380
10. Back Matter
Pages 381-400

### Introduction

One of my favorite graduate courses at Berkeley is Math 251, a one-semester course in ring theory offered to second-year level graduate students. I taught this course in the Fall of 1983, and more recently in the Spring of 1990, both times focusing on the theory of noncommutative rings. This book is an outgrowth of my lectures in these two courses, and is intended for use by instructors and graduate students in a similar one-semester course in basic ring theory. Ring theory is a subject of central importance in algebra. Historically, some of the major discoveries in ring theory have helped shape the course of development of modern abstract algebra. Today, ring theory is a fer­ tile meeting ground for group theory (group rings), representation theory (modules), functional analysis (operator algebras), Lie theory (enveloping algebras), algebraic geometry (finitely generated algebras, differential op­ erators, invariant theory), arithmetic (orders, Brauer groups), universal algebra (varieties of rings), and homological algebra (cohomology of rings, projective modules, Grothendieck and higher K-groups). In view of these basic connections between ring theory and other branches of mathemat­ ics, it is perhaps no exaggeration to say that a course in ring theory is an indispensable part of the education for any fledgling algebraist. The purpose of my lectures was to give a general introduction to the theory of rings, building on what the students have learned from a stan­ dard first-year graduate course in abstract algebra.

### Keywords

Abstract algebra Group theory Representation theory algebra ring theory

#### Authors and affiliations

• T. Y. Lam
• 1
1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4684-0406-7
• Copyright Information Springer-Verlag New York 1991
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4684-0408-1
• Online ISBN 978-1-4684-0406-7
• Series Print ISSN 0072-5285