Noncommutative Noetherian Rings
2001
American Mathematical Society (Verlag)
978-0-8218-2169-5 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-2169-5 (ISBN)
Presents an account of noncommutative Noetherian rings. This book 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.
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.
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.
Preliminaries Basic theory: Some Noetherian rings Quotient rings and Goldie's theorem Structure of semiprime Goldie rings Semiprime ideals in Noetherian rings Some Dedekind-like rings Dimensions: Krull dimension Global dimension Gelfand-Kirillov dimension Extensions: The Nullstellensatz Prime ideals in extension rings Stability $K_0$ and extension rings Examples: Polynomial identity rings Enveloping algebras of Lie algebras Rings of differential operators on algebraic varieties References Index of notation Index.
| Erscheint lt. Verlag | 1.8.2002 |
|---|---|
| Reihe/Serie | Graduate Studies in Mathematics |
| Zusatzinfo | Illustrations |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 1361 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 0-8218-2169-5 / 0821821695 |
| ISBN-13 | 978-0-8218-2169-5 / 9780821821695 |
| Zustand | Neuware |
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