Algebraic Number Fields
Published on 15. August 1973
219 pages
978-0-08-087370-1 (ISBN)
Description
Algebraic Number Fields
More details
Other editions
Additional editions
Gerald J. Janusz
Algebraic Number Fields
Book
01/1973
Academic Press
€52.62
Article exhausted; check different version
Persons
Content
- Front Cover
- Algebraic Number Fields
- Copyright Page
- Contents
- Preface
- Chapter I. Subrings of Fields
- 1. Localization
- 2. Integral Dependence
- 3. Discrete Valuation Rings and Dedekind Rings
- 4. Fractional Ideals and the Class Group
- 5. Norms and Traces
- 6. Extensions of Dedekind Rings
- 7. Discriminant
- 8. Norms of Ideals
- 9. Cyclotomic Fields
- 10. Lattices in Real Vector Spaces
- 11. The Unit Theorem and Finiteness of the Class Number
- Chapter II. Complete Fields
- 1. Valuations
- 2. Completions
- 3. Extensions of Nonarchimedean Valuations
- 4. Archimedean Valuations
- 5. Local Norms and Traces and the Product Formula
- Chapter III. Decomposition Groups and the Artin Map
- 1. Decomposition and Inertia Groups
- 2. The Frobenius Automorphism
- 3. The Artin Map for Abelian Extensions
- Chapter IV. Analytic Methods
- 1. Moduli and Ray Classes
- 2. Dirichlet Series
- 3. Characters of Abelian Groups
- 4. L-Series and Product Representations
- 5. Frobenius Density Theorem
- Chapter V. Class Field Theory
- 1. Cohomology of Cyclic Groups
- 2. Preparations for the Second Inequality
- 3. A Norm Index Computation
- 4. The Fundamental Equality for Cyclic Extensions
- 5. The Reciprocity Theorem
- 6. Ideal Groups, Conductors, and Class Fields
- 7. Reduction Steps Toward the Existence Theorem
- 8. Kummer Extensions and The S-Unit Theorem
- 9. The Existence Theorem
- 10. Some Consequences of the Classification Theorem
- 11. Preliminaries for the Norm Residue Map and the Conductor Theorem
- 12. Norm Residue Symbol
- 13. The Hilbert Class Field
- Chapter VI. Application of the General Theory to Quadratic Fields
- 1. The Conductor of Q(Vd)
- 2. Two Examples
- 3. The Extended Class Group
- Appendix A. Normal Basis Theorem and Hilbert's Theorem 90
- Appendix B. Modules over Principal Ideal Domains
- Bibliography
- Index
