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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 |
MARC
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| 100 | 1 | |a Goodearl, K. R. | |
| 245 | 1 | 3 | |a An introduction to noncommutative Noetherian rings / |c K.R. Goodearl, R.B. Warfield, Jr. |
| 250 | |a 2nd ed. | ||
| 260 | |a Cambridge, U.K. ; |a New York : |b Cambridge University Press, |c 2004. | ||
| 300 | |a 1 online resource (xxiv, 344 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 490 | 1 | |a London Mathematical Society student texts ; |v 61 | |
| 504 | |a Includes bibliographical references (pages 328-337) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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 throughout. Various important settings, such as group algebras, Lie algebras, and quantum groups, are sketched at the outset to describe typical problems and provide motivation. The text then develops and illustrates the standard ingredients of the theory: e.g., skew polynomial rings, rings of fractions, bimodules, Krull dimension, linked prime ideals. Recurring emphasis is placed on prime ideals, which play a central role in applications to representation theory. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. Material includes the basic types of quantum groups, which then serve as test cases for the theory developed. | ||
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Noetherian rings. | |
| 650 | 0 | |a Noncommutative rings. | |
| 650 | 6 | |a Anneaux noethériens. | |
| 650 | 6 | |a Anneaux non commutatifs. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Noetherian rings |2 fast | |
| 650 | 7 | |a Noncommutative rings |2 fast | |
| 650 | 7 | |a Nichtkommutativer Noetherscher Ring |2 gnd | |
| 700 | 1 | |a Warfield, Robert B., |d 1940- | |
| 776 | 0 | 8 | |i Print version: |a Goodearl, K.R. |t Introduction to noncommutative Noetherian rings. |b 2nd ed. |d Cambridge, U.K. ; New York : Cambridge University Press, 2004 |z 0521836875 |w (DLC) 2003065357 |w (OCoLC)53231332 |
| 830 | 0 | |a London Mathematical Society student texts ; |v 61. | |
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