Number Theory /

Number Theory / / Helmut Hasse.

Show other versions (1)
Saved in:
Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter DGBA Mathematics - <1990
VerfasserIn:
Hasse, Helmut,
Place / Publishing House:Berlin ;, Boston : : De Gruyter, , [2022]
©1979
Year of Publication:2022
Edition:English Translation. Edited and Prepared for Publication by Horst Giinter Zimmer, Reprint 2021
Language:English
Online Access:
Physical Description:1 online resource (658 p.) :; 49 Fig.
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • Frontmatter
  • Preface to the English Edition
  • Preface to the First Edition
  • Preface to the Second Edition
  • Preface to the Third Edition
  • Table of Contents
  • Part I The Foundations of Arithmetic in the Rational Number Field
  • Chapter 1. Prime Decomposition
  • Chapter 2. Divisibility
  • Chapter 3. Congruences
  • Chapter 4. The Structure of the Residue Class Ring mod m and of the Reduced Residue Class Group mod m
  • Chapter 5. Quadratic Residues
  • Part II The Theory of Valued Fields
  • Chapter 6. The Fundamental Concepts Regarding Valuations
  • Chapter 7. Arithmetic in a Discrete Valued Field
  • Chapter 8. The Completion of a Valued Field
  • Chapter 9. The Completion of a Discrete Valued Field. The p-adie Number Fields
  • Chapter 10. The Isomorphism Types of Complete Discrete Valued Fields with Perfect Residue Class Field
  • Chapter 11. Prolongation of a Discrete Valuation to a Purely Transcendental Extension
  • Chapter 12. Prolongation of the Valuation of a Complete Field to a Finite-Algebraic Extension
  • Chapter 13. The Isomorphism Types of Complete Archimedean Valued Fields
  • Chapter 14. The Structure of a Finite-Algebraic Extension of a Complete Discrete Valued Field
  • Chapter 15. The Structure of the Multiplicative Group of a Complete Discrete Valued Field with a Perfect Residue Class Field of Prime Characteristic
  • Chapter 16. The Tamely Ramified Extension Types of a Complete Discrete Valued Field with Finite Residue Class Field of Characteristic p
  • Chapter 17. The Exponential Function, the Logarithm, and Powers in a Complete Non-Archimedean Valued Field of Characteristic Zero
  • Chapter 18. Prolongation of the Valuation of a Non-Complete Field to a Finite-Algebraic Extension
  • Part III The Foundations of Arithmetic in Algebraic Number Fields
  • Chapter 19. Relations Between the Complete System of Valuations and the Arithmetic of the Rational Number Field
  • Chapter 20. Prolongation of the Complete System of Valuations to a Finite-Algebraic Extension
  • Chapter 21. The Prime Spots of an Algebraic Number Field and their Completions
  • Chapter 22. Decomposition into Prime Divisors, Integrality, and Divisibility
  • Chapter 23. Congruences
  • Chapter 24. The Multiples of a Divisor
  • Chapter 25. Differents and Discriminants
  • Chapter 26. Quadratic Number Fields
  • Chapter 27. Cyclotomic Fields
  • Chapter 28. Units
  • Chapter 29. The Class Number
  • Chapter 30. Approximation Theorems and Estimates for the Discriminant
  • Index of Names
  • Subject Index

Similar Items