This self-contained graduate text provides a readily available source of information and reference for a substantial part of ring theory developed over the last 80 years. The book completes a trilogy with the authors A First Course in Noncommutative Rings and Lectures on Modules and Rings. It deals with a number of current topics in noncommutative algebra, ranging from von Neumann regular rings, unit-regular rings and strongly regular rings, exchange (or "suitable") rings, to clean, strongly clean, and nil-clean rings, with a dosage of the popular theory of generalized inverses (including Drazin inverses and MoorePenrose inverses) in between.
Following all of the above ring-theoretic "excursions", the text concludes with a final chapter on the issues of cancellation and substitution of modules, along with a discussion on the relatively classical stable range theory of rings. The rich exercise sets for the various chapters of the book are designed to be especially helpful for students and researchers alike who desire to deepen their understanding of noncommutative algebra.
Chapter
1. Introduction to Regular Rings.
Chapter
2. Fitting Theory and
Modules Over Regular Rings.
Chapter
3. Generalized Inverses and Rings with
Involutions.
Chapter
4. Exchange Rings and Suitable Rings.
Chapter
5. Clean
Rings and their Variations.
Chapter
6. Cancellation, Substitution, and
Stable Range.
T. Y. Lam is a professor emeritus of mathematics at the University of California, Berkeley. His research interests are broadly spread across group theory, ring theory, field theory, and the history of mathematics. With the past support of a Sloan Fellowship, a Guggenheim Fellowship, and a UCB Miller Professorship, he has published 143 papers and 12 books, to date. A winner of the Leroy Steele Prize for mathematical exposition in 1982, Lam's scholarly work has so far received 6371 MathSciNet citations and 19723 Google Scholar citations.
