Weyl Algebraic Theory of Numbers

1. Auflage 2016
ISBN: 978-1-4008-8280-9
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 40, 240 Seiten

Reihe: Annals of Mathematics StudiesPrinceton Landmarks in Mathematics and Physics

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.

Autoren/Hrsg.

Weyl, Hermann

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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

Über Autor(innen)

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.