A First Course in Noncommutative Rings, an outgrowth of the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-semester course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semisimple rings, Jacobson's theory of the radical, representation theory of groups and algebras, prime and semiprime rings, local and semilocal rings, perfect and semiperfect rings, etc. By aiming the level of writing at the novice rather than the connoisseur and by stressing th the role of examples and motivation, the author has produced a text that is suitable not only for use in a graduate course, but also for self- study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.
From the reviews of the second edition:
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."
"Ten years ago, the first edition ... of this book appeared. It is quite rare that a book can become a classic in such a short time, but this did happen for this excellent book. Of course minor changes were made for the second edition; new exercises and an appendix on uniserial modules were added. Every part of the text was written with love and care. The explanations are very well done, useful examples help to understand the material ... ." (G. Pilz, Internationale Mathematische Nachrichten, Issue 196, 2004)
"The present book is a radical update. For the second edition the text was retyped, some proofs were rewritten and improvements in exposition have also taken place. ... It is well-written and consists of eight chapters. ... There is a very good reference section for further study and a name index consisting of four pages of closely-packed names. ... As always the standard of print and presentation by Springer is exemplary." (Brian Denton, The Mathematical Gazette, Vol. 86 (505), 2002)
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."
"Ten years ago, the first edition ... of this book appeared. It is quite rare that a book can become a classic in such a short time, but this did happen for this excellent book. Of course minor changes were made for the second edition; new exercises and an appendix on uniserial modules were added. Every part of the text was written with love and care. The explanations are very well done, useful examples help to understand the material ... ." (G. Pilz, Internationale Mathematische Nachrichten, Issue 196, 2004)
"The present book is a radical update. For the second edition the text was retyped, some proofs were rewritten and improvements in exposition have also taken place. ... It is well-written and consists of eight chapters. ... There is a very good reference section for further study and a name index consisting of four pages of closely-packed names. ... As always the standard of print and presentation by Springer is exemplary." (Brian Denton, The Mathematical Gazette, Vol. 86 (505), 2002)