| 000 | 00000cam u2200205 a 4500 | |
| 001 | 000000667357 | |
| 005 | 20151022112503 | |
| 008 | 980819s1998 gw b 001 0 eng | |
| 010 | ▼a 98042185 | |
| 020 | ▼a 3540627790 (alk. paper) | |
| 040 | ▼a DLC ▼c DLC ▼d UKM ▼d 211009 | |
| 041 | 1 | ▼a eng ▼h ger |
| 049 | ▼l 111160986 | |
| 050 | 0 0 | ▼a QA247 ▼b .H5313 1998 |
| 082 | 0 0 | ▼a 512/.74 ▼2 21 |
| 084 | ▼a 512.74 ▼2 DDCK | |
| 090 | ▼a 512.74 ▼b H641tE | |
| 100 | 1 | ▼a Hilbert, David, ▼d 1862-1943. |
| 240 | 1 0 | ▼a Theorie der algebraischen Zahlkörper. ▼l English |
| 245 | 1 4 | ▼a The theory of algebraic number fields / ▼c David Hilbert ; translated from the German by Iain T. Adamson ; with an introduction from Franz Lemmermeyer and Norbert Schappacher. |
| 260 | ▼a Berlin ; ▼a New York : ▼b Springer, ▼c c1998. | |
| 300 | ▼a xxxvi, 350 p. ; ▼c 25 cm. | |
| 504 | ▼a Includes bibliographical references (p. [335]-343) and index. | |
| 650 | 0 | ▼a Algebraic fields. |
Holdings Information
| No. | Location | Call Number | Accession No. | Availability | Due Date | Make a Reservation | Service |
|---|---|---|---|---|---|---|---|
| No. 1 | Location Main Library/Western Books/ | Call Number 512.74 H641tE | Accession No. 111160986 | Availability Available | Due Date | Make a Reservation | Service |
Contents information
Table of Contents
1. Algebraic Numbers and Number Fields.- 2. Ideals of Number Fields.- 3. Congruences with Respect to Ideals.- 4. The Discriminant of a Field and its Divisors.- 5. Extension Fields.- 6. Units of a Field.- 7. Ideal Classes of a Field.- 8. Reducible Forms of a Field.- 9. Orders in a Field.- 10. Prime Ideals of a Galois Number Field and its Subfields.- 11. The Differents and Discriminants of a Galois Number Field and its Subfields.- 12. Connexion Between the Arithmetic and Algebraic Properties of a Galois Number Field.- 13. Composition of Number Fields.- 14. The Prime Ideals of Degree 1 and the Class Concept.- 15. Cyclic Extension Fields of Prime Degree.- 16. Factorisation of Numbers in Quadratic Fields.- 17. Genera in Quadratic Fields and Their Character Sets.- 18. Existence of Genera in Quadratic Fields.- 19. Determination of the Number of Ideal Classes of a Quadratic Field.- 20. Orders and Modules of Quadratic Fields.- 21. The Roots of Unity with Prime Number Exponent l and the Cyclotomic Field They Generate.- 22. The Roots of Unity for a Composite Exponent m and the Cyclotomic Field They Generate.- 23. Cyclotomic Fields as Abelian Fields.- 24. The Root Numbers of the Cyclotomic Field of the l-th Roots of Unity.- 25. The Reciprocity Law for l-th Power Residues Between a Rational Number and a Number in the Field of l-th Roots of Unity.- 26. Determination of the Number of Ideal Classes in the Cyclotomic Field of the m-th Roots of Unity.- 27. Applications of the Theory of Cyclotomic Fields to Quadratic Fields.- 28. Factorisation of the Numbers of the Cyclotomic Field in a Kummer Field.- 29. Norm Residues and Non-residues of a Kummer Field.- 30. Existence of Infinitely Many Prime Ideals with Prescribed Power Characters in a Kummer Field.- 31. Regular Cyclotomic Fields.- 32. Ambig Ideal Classes and Genera in Regular Kummer Fields.- 33. The l-th Power Reciprocity Law in Regular Cyclotomic Fields.- 34. The Number of Genera in a Regular Kummer Field.- 35. New Foundation of the Theory of Regular Kummer Fields.- 36. The Diophantine Equation ?m + ?m + ?m = 0.- References.- List of Theorems and Lemmas.
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