Author(s): Nicolas Bourbaki
Series: Elements of Mathematics
Edition: 1
Publisher: Hermann / Addison-Wesley
Year: 1972
Language: English
Commentary: new scan
City: Paris; Reading, MA
Title
To the reader
Contents of The Elements of Mathematics Series
Contents
Introduction
I. Flat Modules
1. Diagrams and exact sequences
2. Flat modules
3. Faithfully flat modules
4. Flat modules and "Tor" functors
Exercises
II. Localization
1. Prime ideals
2. Rings and modules of fractions
3. Local rings. Passage from the local to the global
4. Spectra of rings and supports of modules
5. Finitely generated projective modules. Invertible fractional ideals
Exercises
III. Graduations, Filtrations and Topologies
1. Finitely generated graded algebras
2. General results on filtered rings and modules
3. m-adic topologies on Noetherian rings
4. Lifting in complete rings
5. Flatness properties of filtered modules
Exercises
IV. Associated Prime Ideals and Primary Decomposition
1. Prime ideals associated with a module
2. Primary decomposition
3. Primary decomposition in graded modules
Exercises
V. Integers
1. Notion of an integral element
2. The lift of prime ideals
3. Finitely generated algebras over a field
Exercises
VI. Valuations
1. Valuation rings
2. Places
3. Valuations
4. The height of a valuation
5. The topology defined by a valuation
6. Absolute values
7. The approximation theorem
8. Extensions of a valuation to an algebraic extension
9. Application: Locally compact fields
10. Extensions of a valuation to a transcendental extension
Exercises
VII. Divisors
1. Krull domains
2. Dedekind domains
3. Factorial domains
4. Modules over integrally closed Noetherian domains
Exercises
Historical note
Bibliography
Index of notation
Index of terminology
Table of implications
Table of invariances - I
Table of invariances - II
