An Introduction to Noncommutative Noetherian Rings

ISBN-13: 9780521545372 / Angielski / Miękka / 2004 / 370 str.

K. R. Goodearl; Robert B. Warfield

Opis

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.

Recenzje

'… 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 MATH

Spis treści

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.