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An introduction to noncommutative Noetherian rings /
This 2004 introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throu...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, U.K. ; New York :
Cambridge University Press,
2004.
|
| Edición: | 2nd ed. |
| Colección: | London Mathematical Society student texts ;
61. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover
- Series-title
- Title
- Copyright
- Contents
- Introduction to the Second Edition
- Introduction to the First Edition
- Prologue
- POLYNOMIAL IDENTITY RINGS
- GROUP ALGEBRAS
- RINGS OF DIFFERENTIAL OPERATORS
- ENVELOPING ALGEBRAS
- QUANTUM GROUPS
- NOTATION AND TERMINOLOGY
- 1. A Few Noetherian Rings
- THE NOETHERIAN CONDITION
- FORMAL TRIANGULAR MATRIX RINGS
- THE HILBERT BASIS THEOREM
- SKEW POLYNOMIAL RINGS TWISTED BY AUTOMORPHISMS
- SKEW-LAURENT RINGS
- SIMPLICITY IN SKEW-LAURENT RINGS
- ADDITIONAL EXERCISES.
- NOTES
- 2. Skew Polynomial Rings
- FORMAL DIFFERENTIAL OPERATOR RINGS
- WEYL ALGEBRAS
- GENERAL SKEW POLYNOMIAL RINGS
- A GENERAL SKEW HILBERT BASIS THEOREM
- SOME EXAMPLES
- ADDITIONAL EXERCISES
- NOTES
- 3. Prime Ideals
- PRIME IDEALS
- SEMIPRIME IDEALS AND NILPOTENCE
- ANNIHILATORS AND ASSOCIATED PRIME IDEALS
- SOME EXAMPLES FROM REPRESENTATION THEORY
- PRIMITIVE AND SEMIPRIMITIVE IDEALS
- PRIME IDEALS IN DIFFERENTIAL OPERATOR RINGS
- ADDITIONAL EXERCISES
- NOTES.
- 4. Semisimple Modules, Artinian Modules, and Torsionfree Modules
- SEMISIMPLE MODULES
- SEMISIMPLE RINGS
- ARTINIAN MODULES
- ARTINIAN RINGS
- TORSION AND TORSIONFREE MODULES
- NOTES
- 5. Injective Hulls
- INJECTIVE MODULES
- ESSENTIAL EXTENSIONS
- INJECTIVE HULLS
- MODULES OF FINITE RANK
- UNIFORM RANK
- DIRECT SUMS OF INJECTIVE MODULES
- ASSASSINATOR PRIMES
- ADDITIONAL EXERCISES
- NOTES
- 6. Semisimple Rings of Fractions
- RINGS OF FRACTIONS
- DIVISION RINGS OF FRACTIONS
- GOLDIE'S THEOREM.
- NIL SUBSETS
- ADDITIONAL EXERCISES
- NOTES
- 7. Modules over Semiprime Goldie Rings
- MINIMAL PRIME IDEALS
- TORSION
- TORSIONFREE INJECTIVE MODULES
- TORSIONFREE UNIFORM MODULES
- TORSIONFREE MODULES OVER PRIME GOLDIE RINGS
- NOTES
- 8. Bimodules and A.liated Prime Ideals
- NOETHERIAN BIMODULES
- AFFILIATED PRIME IDEALS
- ARTINIAN BIMODULES
- PRIME IDEALS IN FINITE RING EXTENSIONS
- BIMODULE COMPOSITION SERIES
- ADDITIVITY PRINCIPLES
- NORMALIZING EXTENSIONS
- NOTES
- 9. Fully Bounded Rings
- BOUNDEDNESS.
- EMBEDDING MODULES INTO FACTOR RINGS
- ARTINIAN MODULES
- UNIFORM INJECTIVE MODULES
- NOTES
- 10. Rings and Modules of Fractions
- RINGS OF FRACTIONS
- MODULES OF FRACTIONS
- SUBMODULES OF MODULES OF FRACTIONS
- IDEALS IN RINGS OF FRACTIONS
- PRIME IDEALS IN ITERATED DIFFERENTIAL OPERATOR RINGS
- ADDITIONAL EXERCISES
- NOTES
- 11. Artinian Quotient Rings
- REDUCED RANK
- APPLICATIONS OF REDUCED RANK TO FINITE RING EXTENSIONS
- SMALL'S THEOREM
- AFFILIATED PRIME IDEALS
- AFFILIATED PRIME IDEALS
- NOTES.