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The theory of algebraic number fields

The theory of algebraic number fields (2회 대출)

자료유형
단행본
개인저자
Hilbert, David, 1862-1943.
서명 / 저자사항
The theory of algebraic number fields / David Hilbert ; translated from the German by Iain T. Adamson ; with an introduction from Franz Lemmermeyer and Norbert Schappacher.
발행사항
Berlin ;   New York :   Springer,   c1998.  
형태사항
xxxvi, 350 p. ; 25 cm.
ISBN
3540627790 (alk. paper)
서지주기
Includes bibliographical references (p. [335]-343) and index.
일반주제명
Algebraic fields.
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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
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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.

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/서고7층/ 청구기호 512.74 H641tE 등록번호 111160986 도서상태 대출가능 반납예정일 예약 서비스 B M

컨텐츠정보

목차

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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