An Introduction to Noncommutative Noetherian Rings
An Introduction to Noncommutative Noetherian Rings
This introduction to noncommutative noetherian rings, accessible to anyone with a basic background in abstract algebra, can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory material is given, and exercises are integrated throughout. New material includes the basic types of quantum groups.
- Sketches of typical classes of application for motivation
- Extensive explanatory discussion
- Exercises integrated throughout the text
Reviews & endorsements
"Readers of the first edition will notice a number of changes in this edition, including a restrucuring of the topics, many more explicit examples, and an increased emphasis on quantum groups, a subject which has flourished in the decade that has passed since the first edition...This level of explicitness would make large parts of the book accessible even to an undergraduate who has only completed a first course in algebra, although the target audience is primarily at the graduate student level."
MAA Reviews, Darren Glass
Product details
July 2006Adobe eBook Reader
9780511208348
0 pages
0kg
375 exercises
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- 1. A few Noetherian rings
- 2. Skew polynomial rings
- 3. Prime ideals
- 4. Semisimple modules, Artinian modules, and torsionfree modules
- 5. Injective hulls
- 6. Semisimple rings of fractions
- 7. Modules over semiprime Goldie rings
- 8. Bimodules and affiliated prime ideals
- 9. Fully bounded rings
- 10. Rings and modules of fractions
- 11. Artinian quotient rings
- 12. Links between prime ideals
- 13. The Artin-Rees property
- 14. Rings satisfying the second layer condition
- 15. Krull dimension
- 16. Numbers of generators of modules
- 17. Transcendental division algebras.
