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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
Table of Contents
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Front/Back Matter
Chapters
- Chapter 0. Preliminaries
Part I. Basic theory
- Chapter 1. Some Noetherian rings
- Chapter 2. Quotient rings and Goldieās 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