An introduction to noncommutative noetherian rings
著者
書誌事項
An introduction to noncommutative noetherian rings
（London Mathematical Society student texts, 16）
Cambridge University Press, 1989
- : hard
- : pbk
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: hard410.8//L84//161890136480,
: pbk410.8//L84//16192022235, 410.8//L84//16189013648 -
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注記
Includes bibliographical references (p. [291]-298) and index
内容説明・目次
内容説明
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.
目次
- 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.
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