Local Algebra
The present book is an English translation of Algebre Locale - Multiplicites published by Springer-Verlag as no. 11 of the Lecture Notes series. The original text was based on a set of lectures, given at the College de France in 1957-1958, and written up by Pierre Gabriel. Its aim was to give a shor...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2000, 2000
|
| Edition: | 1st ed. 2000 |
| Series: | Springer Monographs in Mathematics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I. Prime Ideals and Localization
- §1. Notation and definitions
- §2. Nakayama’s lemma
- §3. Localization
- §4. Noetherian rings and modules
- §5. Spectrum
- §6. The noetherian case
- §7. Associated prime ideals
- §8. Primary decompositions
- II. Tools
- A: Filtrations and Gradings
- B: Hilbert-Samuel Polynomials
- III. Dimension Theory
- A: Dimension of Integral Extensions
- B: Dimension in Noetherian Rings
- C: Normal Rings
- D: Polynomial Rings
- IV. Homological Dimension and Depth
- A: The Koszul Complex
- B: Cohen-Macaulay Modules
- C: Homological Dimension and Noetherian Modules
- D: Regular Rings
- Appendix I: Minimal Resolutions
- Appendix II: Positivity of Higher Euler-Poincaré Characteristics
- Appendix III: Graded-polynomial Algebras
- V. Multiplicities
- A: Multiplicity of a Module
- B: Intersection Multiplicity of Two Modules
- C: Connection with Algebraic Geometry
- Index of Notation