An Introduction to Noncommutative Noetherian Rings

2. Auflage 2011
ISBN: 978-0-521-83687-6
Verlag: Cambridge University Press

Buch, Englisch, Band 61, 368 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 751 g

Reihe: London Mathematical Society Student Texts

This introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. Various important settings, such as group algebras, Lie algebras, and quantum groups, are sketched at the outset to describe typical problems and provide motivation. The text then develops and illustrates the standard ingredients of the theory: e.g., skew polynomial rings, rings of fractions, bimodules, Krull dimension, linked prime ideals. Recurring emphasis is placed on prime ideals, which play a central role in applications to representation theory. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. New material includes the basic types of quantum groups, which then serve as test cases for the theory developed.

Autoren/Hrsg.

Goodearl, Kenneth R.

Goodearl, K. R.

Warfield, Jr.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

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.

Über Autor(innen)

Warfield, Jr.
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.

Goodearl, K. R.
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.