An Introduction to Noncommutative Noetherian Rings
Seiten
1989
Cambridge University Press (Verlag)
978-0-521-36086-9 (ISBN)
Cambridge University Press (Verlag)
978-0-521-36086-9 (ISBN)
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This introduction is intended to be accessible to anyone with a basic background in algebra and can be used as a first-year graduate text, or a self-contained reference. The standard techniques in the area (ring of fractions, bimodules, Krull dimension, linked prime ideals) are introduced and applied to a variety of problems.
This introduction to noncommutative Noetherian rings is intended to be accessible to anyone with a basic background in algebra. It can be used as a first-year graduate text, or as a self-contained reference. The authors' pedagogic style, with much explanatory discussion and exercises integrated into the development, will be a valuable aid in this respect. The standard techniques in the area (rings of fractions, bimodules, Krull dimension, linked prime ideals) are introduced and applied to a variety of problems. A recurring emphasis is placed on prime ideals and injective modules.
This introduction to noncommutative Noetherian rings is intended to be accessible to anyone with a basic background in algebra. It can be used as a first-year graduate text, or as a self-contained reference. The authors' pedagogic style, with much explanatory discussion and exercises integrated into the development, will be a valuable aid in this respect. The standard techniques in the area (rings of fractions, bimodules, Krull dimension, linked prime ideals) are introduced and applied to a variety of problems. A recurring emphasis is placed on prime ideals and injective modules.
Introduction; Prologue; 1. A few Noetherian rings; 2. Prime ideals; 3. Semisimple modules, Artinian modules, and nonsingular modules; 4. Injective hulls; 5. Semisimple rings of fractions; 6. Modules over semiprime goldie rings; 7. Bimodules and affiliated prime ideals; 8. Fully bounded rings; 9. Rings of fractions; 10. Artinian quotient rings; 11. Links between prime ideals; 12. Rings satisfying the second layer condition; 13. Krull dimension; 14. Numbers of generators of modules; 15. Transcendental division algebras; Appendix.
| Erscheint lt. Verlag | 24.8.1989 |
|---|---|
| Reihe/Serie | London Mathematical Society Student Texts |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 156 x 235 mm |
| Gewicht | 564 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 0-521-36086-2 / 0521360862 |
| ISBN-13 | 978-0-521-36086-9 / 9780521360869 |
| Zustand | Neuware |
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