A First Course in Noncommutative Rings

Graduate Texts in Mathematics #131

by T.Y. Lam

MATHEMATICAL REVIEWS "This is a textbook for graduate students who have had an introduction to abstract algebra and now wish to study noncummutative rig theory...there is a feeling that each topic is presented with specific goals in mind and that the most efficient path is taken to achieve these goals. The author received the Steele prize for mathematical exposition in 1982; the exposition of this text is also award-wining caliber. Although there are many books in print that deal with various aspects of ring theory, this book is distinguished by its quality and level of presentation and by its selection of material....This book will surely be the standard textbook for many years to come. The reviewer eagerly awaits a promised follow-up volume for a second course in noncummutative ring theory."

Genres: Mathematics, Algebra

397 pages, Hardcover

First published January 1, 1991

Reviews

[Ryan Schwiebert · Rating 5 out of 5]

This is an awesome book for graduates and undergraduates who are fascinated by ring theory. I still use it all the time, and it was indispensable during my own graduate study.

The author has a very readable exposition style, and provides lots of clear examples and useful exercises. As a reader I really felt I was being taken on a purposeful stroll of ideas in ring theory.

In addition to "the staples" of noncommutative ring theory (the Artin-Wedderburn theorem and the Jacobson Density theorem) the book also goes into semiperfect and perfect rings and their cousins. This is the best introduction to such rings that I know of, since most other resources are basically at graduate level.

I saw one review complaining about terminology, but I will contradict the complaint wholeheartedly. The author's definitions and presentation are very clear and they are all completely within mainstream tolerance.

[Anne · Rating 1 out of 5]

The author doesn't define his terms, which makes the book a trial to read. I appreciate that reiterating basic definitions takes up space, but some terms are not used in the same way by everyone; in particular, definitions involving "right" and "left" are relative and likely to be variable.

Emblematic is the beginning of page 3: The author says "we have to differentiate carefully between left ideals and right ideals in R" -- and then fails to do so!

Also, the frequent usage of the phrase "quotienting out the ideal" sets my teeth on edge.

[Kolya Matteo · Rating 1 out of 5]

The author doesn't define his terms, which makes the book a trial to read. I appreciate that reiterating basic definitions takes up space, but some terms are not used in the same way by everyone; in particular, definitions involving "right" and "left" are relative and likely to be variable.

Emblematic is the beginning of page 3: The author says "we have to differentiate carefully between left ideals and right ideals in R" -- and then fails to do so!

Also, the frequent usage of the phrase "quotienting out the ideal" sets my teeth on edge.