Algebraic Theory of Numbers
Seiten
1998
Princeton University Press (Verlag)
978-0-691-05917-4 (ISBN)
Princeton University Press (Verlag)
978-0-691-05917-4 (ISBN)
Explores fundamental concepts in arithmetic. This book begins with the definitions and properties of algebraic fields. It then discusses the theory of divisibility from an axiomatic viewpoint, rather than by the use of ideals. It also gives an introduction to p-adic numbers and their uses, which are important in modern number theory.
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.
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.
Hermann Weyl held the chair of mathematics at Zyrich Technische Hochschule from 1913 to 1930; from 1930 to 1933 he held the chair of mathematics at the University of Göttingen; and from 1933 until he retired in 1952 he was a Permanent Member of the Institute for Advanced Study in Princeton.
Ch. I Algebraic Fields 1 Ch. II Theory of Divisibility (Kronecker, Dedekind) 33 Ch. III Local Primadic Analysis (Kummer, Hensel) 71 Ch. IV Algebraic Number Fields 141 Amendments 223
| Erscheint lt. Verlag | 10.5.1998 |
|---|---|
| Reihe/Serie | Annals of Mathematics Studies |
| Zusatzinfo | 30 halftones |
| Verlagsort | New Jersey |
| Sprache | englisch |
| Maße | 152 x 235 mm |
| Gewicht | 340 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| ISBN-10 | 0-691-05917-9 / 0691059179 |
| ISBN-13 | 978-0-691-05917-4 / 9780691059174 |
| Zustand | Neuware |
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