Noncommutative Noetherian Rings (Graduate Studies in Mathematics)

This is an updated edition of a work that was considered the definitive account in the subject area upon its initial publication by J. Wiley & Sons in 1987. It presents, within a wider context, a comprehensive account of noncommutative Noetherian rings. The author covers the major developments from the 1950s, stemming from Goldie's theorem and onward, including applications to group rings, enveloping algebras of Lie algebras, PI rings, differential operators, and localization theory. The book is not restricted to Noetherian rings, but discusses wider classes of rings where the methods apply more generally. In the current edition, some errors were corrected, a number of arguments have been expanded, and the references were brought up to date. This reprinted edition will continue to be a valuable and stimulating work for readers interested in ring theory and its applications to other areas of mathematics. Chapter 0. Preliminaries Chapter 1. Some Noetherian Rings Chapter 2. Quotient Rings And Goldie's Theorem Chapter 3. Structure Of Semiprime Goldie Rings Chapter 4. Semiprime Ideals In Noetherian Rings Chapter 5. Some Dedekind-like Rings Chapter 6. Krull Dimension Chapter 7. Global Dimension Chapter 8. Gelfand-kirillov Dimension Chapter 9. The Nullstellensatz Chapter 10. Prime Ideals In Extension Rings Chapter 11. Stability Chapter 12. $k_0$ And Extension Rings Chapter 13. Polynomial Identity Rings Chapter 14. Enveloping Algebras Of Lie Algebras Chapter 15. Rings Of Differential Operators On Algebraic Varieties J.c. Mcconnell, J.c. Robson, With The Cooperation Of L.w. Small. Orginally Published: Chichester [west Sussex] ; New York : Wiley, [1988] C1987. Includes Bibliographical References (p. 595-619) And Index.