# An Introduction to Noncommutative Noetherian Rings

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Juli 2004

## Beschreibung

### Beschreibung

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.### Inhaltsverzeichnis

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.### Portrait

K. R. Goodearl received his Ph.D. in 1971 from the University of Washington. Following an instructorship at the University of Chicago, he spent 19 years at the University of Utah. Since 1991, he has been a professor of mathematics at the University of California at Santa Barbara. R. B. Warfield Jr. received his Ph.D. in 1967 from Harvard University. Following a postdoctoral year at New Mexico State University, he joined the mathematics department of the University of Washington, where he was a professor until his death in 1989.### Pressestimmen

'... well written and perfectly suits for both students beginning to study Ring theory and established mathematicians that are just interested in learning basics of the theory of Noetherian rings.' Zentralblatt MATHEAN: 9780521836876

ISBN: 0521836875

Untertitel: 'London Mathematical Society St'.
Revised.
Sprache: Englisch.

Verlag: CAMBRIDGE UNIV PR

Erscheinungsdatum: Juli 2004

Seitenanzahl: 370 Seiten

Format: gebunden

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