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Algebraic theory of numbers /
In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields, which are relied upon throughout. The theory of divisibility is...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, N.J. :
Princeton University Press,
1998, ©1968.
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| Colección: | Princeton landmarks in mathematics and physics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Weyl, Hermann, |d 1885-1955. | |
| 245 | 1 | 0 | |a Algebraic theory of numbers / |c by Hermann Weyl. |
| 260 | |a Princeton, N.J. : |b Princeton University Press, |c 1998, ©1968. | ||
| 300 | |a 1 online resource (ix, 223 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Princeton landmarks in mathematics and physics | |
| 504 | |a Includes bibliographical references (page ix). | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | 0 | |t Frontmatter -- |t CONTENTS -- |t PREFACE -- |t A SHORT BIBLIOGRAPHY (BOOKS ONLY) -- |t Chapter I. ALGEBRAIC FIELDS -- |t Chapter II. THEORY OF DIVISIBILITY (KRONECKER, DEDEKIND) -- |t Chapter III. LOCAL PRIMADIC ANALYSIS (KUMMER-HENSEL) -- |t Chapter IV. ALGEBRAIC NUMBER FIELDS -- |t ERRATA -- |t AMENDMENTS |
| 520 | |a In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields, which are relied upon throughout. The theory of divisibility is then discussed, from an axiomatic viewpoint, rather than by the use of ideals. There follows an introduction to p-adic numbers and their uses, which are so important in modern number theory, and the book culminates with an extensive examination of algebraic number fields. Weyl's own modest hope, that the work "will be of some use," has more than been fulfilled, for the book's clarity, succinctness, and importance rank it as a masterpiece of mathematical exposition. | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 650 | 0 | |a Algebraic number theory. | |
| 650 | 6 | |a Théorie algébrique des nombres. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x General. |2 bisacsh | |
| 650 | 7 | |a Algebraic number theory. |2 fast |0 (OCoLC)fst00804937 | |
| 776 | 0 | 8 | |i Print version: |z 9781400882809 |
| 830 | 0 | |a Princeton landmarks in mathematics and physics. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctt1b4cws3 |z Texto completo |
| 880 | 0 | |6 505-00/Grek |a Cover; Title; Copyright; CONTENTS; Chapter I. ALGEBRAIC FIELDS; 1. Finite field. Norm, trace, discriminant; 2. Tower. Analysis of the field equation; 3. Simple extension; 4. Relative trace, norm and discriminant; 5. Removal of the hypothesis of separability; 6. The Galois case; 7. Consecutive extensions replaced by a single one; 8. Strictly finite field; 9. Adjunction of Indeterminate; Chapter II. THEORY OF DIVISIBILITY (KRONECKER, DEDEKIND); 1. Integers; 2. Our disbelief in Ideals; 3. The axioms; 4. Consequences; 5. Integrity in ϰ(x, y, .) over k(x, y, .); 6. Kronecker's theory. | |
| 880 | 8 | |6 505-00/Grek |a 7. The fundamental lemma8. A batch of simple propositions; 9. Relative Norm of a Divisor; 10. The Dedekind case; 11. Kronecker and Dedekind; Chapter III. LOCAL PRIMADIC ANALYSIS (KUMMER, HENSEL); 1. Quadratic number field; 2. Kummer's theory: decomposition; 3. Kummer's theory: discriminant; 4. Prime cyclotomic fields; 5. Program; 6. p-adic and y-adic numbers; 7. ϰ(y) and ϰ (J); 8. Discriminant; 9. Relative discriminant; 10. Hilbert's theory of Galois fields. Artin symbol; 11. Cyclotomlc field and quadratic law of reciprocity; 12. General cyclotomic fields; Chapter IV. ALGEBRAIC NUMBER FIELD. | |
| 880 | 8 | |6 505-00/(S |a 1. Lattices (old-fashioned)2. Field basis and basis of an ideal; 3. Norm and number of residues; 4. Euler's function and Fermat's theorem; 5. A new viewpoint; 6. Minkowski's geometric principle; 7. A fundamental inequality and its consequences: existence of ramification ideals, classes of ideals; 8. The Dirichlet-Minkowski-Hasse-Chevalley construction of units; 9. The structure of the group of units; 10. Finite Abelian groups and their characters; 11. Asymptotic equi-distribution of ideals over their classes; 12. ζ-function and related Dirichlet series. | |
| 880 | 8 | |6 505-00/(S |a 13. Prime numbers in residue classes modulo m14. ζ-function of quadratic fields, and their application; 15. Norm residues in quadratic fields; 16. General norm residue symbol and the theory of class fields; Amendments. | |
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