| Algèbre Locale, Multiplicités: Cours Au Collège de France, 1957 - 1958 Contributor(s): Serre, Jean-Pierre (Author), Gabriel, Pierre (Revised by) |
|
 |
ISBN: 3540070281 ISBN-13: 9783540070283 Publisher: Springer OUR PRICE: $31.34 Product Type: Paperback Language: French Published: February 1975 Annotation: This edition reproduces the 2nd corrected printing of the 3rd edition of the now classic notes by Professor Serre, long established as one of the standard introductory texts on local algebra. Referring for background notions to Bourbaki's "Commutative Algebra" (English edition Springer-Verlag 1988), the book focusses on the various dimension theories and theorems on mulitplicities of intersections with the Cartan-Eilenberg functor Tor as the central concept. The main results are the decomposition theorems, theorems of Cohen-Seidenberg, the normalisation of rings of polynomials, dimension (in the sense of Krull) and characteristic polynomials (in the sense of Hilbert-Samuel). |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - General |
| Dewey: 510 |
| Series: Lecture Notes in Mathematics |
| Physical Information: 0.38" H x 6.14" W x 9.21" (0.56 lbs) 160 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Chapitre I. 1DIAUX PIlEMIEIS IT LOCALISATION I I. Wotationa et definitions I 2. Lemme de Bakay. . . . 2 3. Localisation - - - 4. Anneaux et 80dules noethiriens 2 5. Spectre------ 3 4 6. Le cas noetherien. 4 7. Ideaux pre. iers associe. Chapitre 11. OUTILS IT SOUTES A) Filtr-ations et graduations. 8 I. Anneaux et modules filtres - 8 2. Topologie definie par UDe filtration 9 10 3. Coapletion des modules filtres - - - II 4. Anneaux et modules graduis - - - - - 5. au tout redevient noethirien; filtrations -adiques. 15 20 6. Modules differentiels filtres------------ B) Polynoaes de Hilbert-SamueL ----------- 26 I. Rappel sur les polynOmes Ii valeurs entieres---- 26 27 2. Fonctions additives sur les categories de modules. 29 3. Le polynOme caractiristique de Hilbert 32 4. Les invariants de Hilbert-Samuel Chapitre 111. T1I ORlE DE LA DDlE ISION A) Dimension des extensions. entieres. 38 I. Definitions. - - - - - - - - - - - - 38 2. Le premier theore- de Cohen-Seidenberg. 39 3. Le second theoreme de Cohen-Seidenberg - 4I B) Dimension dans les anneaux noetheriens. 43 I. Dimension d'un module. - - - 43 2. Le cas semi-local noetherien 44 3. Syste. es de parametres 47 C) Anneaux normaux 48 I. caracterisation des anneaux normaux. 48 2. Proprietes des anneaux noraaux 51 3. Fermeture integrale. 53 D) Anneaux de polynomes. - - - - - 54 I. |