
Algebraic Number Fields
Description
Alles über E-Books | Antworten auf Fragen rund um E-Books, Kopierschutz und Dateiformate finden Sie in unserem Info- & Hilfebereich.
More details
Other editions
Additional editions
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
System requirements
File format: PDF
Copy protection: Watermark-DRM (Digital Rights Management)
System requirements:
- Computer (Windows; MacOS X; Linux): Use the free software Adobe Reader, Adobe Digital Editions, or any other PDF viewer of your choice (see eBook Help).
- Tablet/Smartphone (Android; iOS): Install the free app Adobe Digital Editions or another reading app for eBooks, e.g., PocketBook (see eBook Help).
- E-reader: Bookeen, Kobo, Pocketbook, Sony, Tolino and many more (only limited: Kindle).
The file format PDF always displays a book page identically on any hardware. This makes PDF suitable for complex layouts such as those used in textbooks and reference books (images, tables, columns, footnotes). Unfortunately, on the small screens of e-readers or smartphones, PDFs are rather annoying, requiring too much scrolling.
This eBook uses Watermark-DRM, a „soft” copy protection. This means that there are no technical restrictions to prevent illegal distribution. However, there is a personalised watermark embedded in the eBook that can be used to identify the purchaser of the eBook in the event of misuse and to provide evidence for legal purposes.
For more information, see our eBook Help page.