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Noncommutative Noetherian Rings

About this Title

J. C. McConnell, University of Leeds, Leeds, England and J. C. Robson, University of Leeds, England

Publication: Graduate Studies in Mathematics
Publication Year: 2001; Volume 30
ISBNs: 978-0-8218-2169-5 (print); 978-1-4704-2084-0 (online)
DOI: https://doi.org/10.1090/gsm/030
MathSciNet review: MR1811901
MSC: Primary 16P40; Secondary 16-02

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Table of Contents

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Front/Back Matter

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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 Dedekind-like rings

Part II. Dimensions

• Chapter 6. Krull dimension
• Chapter 7. Global dimension
• Chapter 8. Gelfand-Kirillov 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