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Hardcover ISBN:  9780821821695 
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Hardcover ISBN:  9780821821695 
Product Code:  GSM/30 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470420840 
Product Code:  GSM/30.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821821695 
eBook ISBN:  9781470420840 
Product Code:  GSM/30.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 

Book DetailsGraduate Studies in MathematicsVolume: 30; 1987; 636 ppMSC: Primary 16;
This is an updated edition of a work that was considered the definitive account in the subject area upon its initial publication by J. Wiley & Sons in 1987. It presents, within a wider context, a comprehensive account of noncommutative Noetherian rings. The author covers the major developments from the 1950s, stemming from Goldie's theorem and onward, including applications to group rings, enveloping algebras of Lie algebras, PI rings, differential operators, and localization theory. The book is not restricted to Noetherian rings, but discusses wider classes of rings where the methods apply more generally. In the current edition, some errors were corrected, a number of arguments have been expanded, and the references were brought up to date. This reprinted edition will continue to be a valuable and stimulating work for readers interested in ring theory and its applications to other areas of mathematics.
ReadershipGraduate students and research mathematicians interested in ring theory and its applications.

Table of Contents

Chapters

Chapter 0. Preliminaries

Part I. Basic theory

Chapter 1. Some Noetherian rings

Chapter 2. Quotient rings and Goldie’s theorem

Chapter 3. Structure of semiprime Goldie rings

Chapter 4. Semiprime ideals in Noetherian rings

Chapter 5. Some Dedekindlike rings

Part II. Dimensions

Chapter 6. Krull dimension

Chapter 7. Global dimension

Chapter 8. GelfandKirillov dimension

Part III. Extensions

Chapter 9. The Nullstellensatz

Chapter 10. Prime ideals in extension rings

Chapter 11. Stability

Chapter 12. $K_0$ and extension rings

Part IV. Examples

Chapter 13. Polynomial identity rings

Chapter 14. Enveloping algebras of Lie algebras

Chapter 15. Rings of differential operators on algebraic varieties


Reviews

A comprehensive list of references (containing more than 500 items) is included.
Mathematica Bohemica 
From reviews of the first edition … A model of mathematical writing, as perfectly written a mathematics book as I have seen … It can be profitably read by nonexperts … an almost perfectly conceived account of major developments and general methods … will remain a basic reference for many years …
Bulletin of the AMS 
Very thorough and illuminating … A veritable tour de force, encompassing a wide range of topics in some depth … very easy to find information in this book … full of illuminating examples which throw a light on [the theory].
Proceedings of the Edinburgh Mathematical Society 
Selfcontained, comprehensive … The creation of this valuable resource is a service to mathematics …
Mathematical Reviews 
An intrinsically interesting branch of algebra … Until … this book there has been no attempt to provide an overview of, and a general reference for, the most important developments in the theory. The … authors set out to fill this gap and have succeeded admirably … easy to read and use … well written … An essential possession for any serious worker in the area.
Zentralblatt MATH 
An account of noncommutative Noetherian rings, giving the theory as far as it exists but with constant emphasis on constructions and examples. [This is] a daunting task but the authors have succeeded well … highly readable … well indexed … will rapidly become the standard text in the field and will stimulate further progress.
Bulletin of the LMS 
An abundance of wellorganized material … a must for those in the area.
International Mathematical News


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This is an updated edition of a work that was considered the definitive account in the subject area upon its initial publication by J. Wiley & Sons in 1987. It presents, within a wider context, a comprehensive account of noncommutative Noetherian rings. The author covers the major developments from the 1950s, stemming from Goldie's theorem and onward, including applications to group rings, enveloping algebras of Lie algebras, PI rings, differential operators, and localization theory. The book is not restricted to Noetherian rings, but discusses wider classes of rings where the methods apply more generally. In the current edition, some errors were corrected, a number of arguments have been expanded, and the references were brought up to date. This reprinted edition will continue to be a valuable and stimulating work for readers interested in ring theory and its applications to other areas of mathematics.
Graduate students and research mathematicians interested in ring theory and its applications.

Chapters

Chapter 0. Preliminaries

Part I. Basic theory

Chapter 1. Some Noetherian rings

Chapter 2. Quotient rings and Goldie’s theorem

Chapter 3. Structure of semiprime Goldie rings

Chapter 4. Semiprime ideals in Noetherian rings

Chapter 5. Some Dedekindlike rings

Part II. Dimensions

Chapter 6. Krull dimension

Chapter 7. Global dimension

Chapter 8. GelfandKirillov dimension

Part III. Extensions

Chapter 9. The Nullstellensatz

Chapter 10. Prime ideals in extension rings

Chapter 11. Stability

Chapter 12. $K_0$ and extension rings

Part IV. Examples

Chapter 13. Polynomial identity rings

Chapter 14. Enveloping algebras of Lie algebras

Chapter 15. Rings of differential operators on algebraic varieties

A comprehensive list of references (containing more than 500 items) is included.
Mathematica Bohemica 
From reviews of the first edition … A model of mathematical writing, as perfectly written a mathematics book as I have seen … It can be profitably read by nonexperts … an almost perfectly conceived account of major developments and general methods … will remain a basic reference for many years …
Bulletin of the AMS 
Very thorough and illuminating … A veritable tour de force, encompassing a wide range of topics in some depth … very easy to find information in this book … full of illuminating examples which throw a light on [the theory].
Proceedings of the Edinburgh Mathematical Society 
Selfcontained, comprehensive … The creation of this valuable resource is a service to mathematics …
Mathematical Reviews 
An intrinsically interesting branch of algebra … Until … this book there has been no attempt to provide an overview of, and a general reference for, the most important developments in the theory. The … authors set out to fill this gap and have succeeded admirably … easy to read and use … well written … An essential possession for any serious worker in the area.
Zentralblatt MATH 
An account of noncommutative Noetherian rings, giving the theory as far as it exists but with constant emphasis on constructions and examples. [This is] a daunting task but the authors have succeeded well … highly readable … well indexed … will rapidly become the standard text in the field and will stimulate further progress.
Bulletin of the LMS 
An abundance of wellorganized material … a must for those in the area.
International Mathematical News