Lectures on Modules and Rings

✍ Scribed by T. Y. Lam (auth.)

• Publisher: Springer-Verlag New York
• Year: 1999
• Tongue: English
• Leaves: 585
• Series: Graduate Texts in Mathematics 189
• Edition: 1
• Category: Library

✦ Synopsis

Textbook writing must be one of the cruelest of self-inflicted tortures. - Carl Faith Math Reviews 54: 5281 So why didn't I heed the warning of a wise colleague, especially one who is a great expert in the subject of modules and rings? The answer is simple: I did not learn about it until it was too late! My writing project in ring theory started in 1983 after I taught a year-long course in the subject at Berkeley. My original plan was to write up my lectures and publish them as a graduate text in a couple of years. My hopes of carrying out this plan on schedule were, however, quickly dashed as I began to realize how much material was at hand and how little time I had at my disposal. As the years went by, I added further material to my notes, and used them to teach different versions of the course. Eventually, I came to the realization that writing a single volume would not fully accomplish my original goal of giving a comprehensive treatment of basic ring theory. At the suggestion of Ulrike Schmickler-Hirzebruch, then Mathematics Editor of Springer-Verlag, I completed the first part of my project and published the write­ up in 1991 as A First Course in Noncommutative Rings, GTM 131, hereafter referred to as First Course (or simply FC).

✦ Table of Contents

Front Matter....Pages i-xxiii
Free Modules, Projective, and Injective Modules....Pages 1-120
Flat Modules and Homological Dimensions....Pages 121-205
More Theory of Modules....Pages 207-286
Rings of Quotients....Pages 287-356
More Rings of Quotients....Pages 357-405
Frobenius and Quasi-Frobenius Rings....Pages 407-457
Matrix Rings, Categories of Modules, and Morita Theory....Pages 459-541
Back Matter....Pages 543-561

✦ Subjects

Algebra