A Classical Invitation to Algebraic Numbers and Class Fields
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1978, 1978
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| Edition: | 1st ed. 1978 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I. Preliminaries
- 1. Introductory Remarks on Quadratic Forms
- 2. Algebraic Background
- 3. Quadratic Euclidean Rings
- 4. Congruence Classes
- 5. Polynomial Rings
- 6. Dedekind Domains
- 7. Extensions of Dedekind Domains
- 8. Rational and Elliptic Functions
- II. Ideal Structure in Number Fields
- 9. Basis and Discriminant
- 10. Prime Factorization
- 11. Units
- 12. Geometry of Numbers
- 13. Finite Determination of Class Number
- III. Introduction to Class Field Theory
- 14. Quadratic Forms, Rings and Genera
- 15. Ray Class Structure and Fields, Hilbert Class Fields
- 16. Hilbert Sequences
- 17 Discriminant and Conductor
- 18. The Artin Isomorphism
- 19. The Zeta-Function
- Appendices (by Olga Taussky)
- Lectures on Class Field Theory by E. Artin (Göttingen 1932) Notes by O. Taussky
- into Connections Between Algebraic Number Theory and Integral Matrices (Appendix by Olga Taussky)
- Subject Matter Index