Number Theory / / Helmut Hasse.

• 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
• Physical Description: 1 online resource (658 p.) :; 49 Fig.
• Other title: 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783112570067; 9783110635881
• DOI: 10.1515/9783112570067
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Helmut Hasse.