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 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.

List of contents

Ch. I Algebraic Fields Ch. II Theory of Divisibility (Kronecker, Dedekind) Ch. III Local Primadic Analysis (Kummer, Hensel) Ch. IV Algebraic Number Fields Amendments

About the author

Hermann Weyl

Summary

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.

Product details

• Authors: Hermann Weyl
• Publisher: Princeton University Press
• Languages: English
• Product format: Paperback / Softback
• Released: 20.04.1998
• EAN: 9780691059174
• ISBN: 978-0-691-05917-4
• No. of pages: 240
• Dimensions: 150 mm x 230 mm x 12 mm
• Series: Annals of Mathematics Studies; Princeton Landmarks in Mathematics and Physics; Princeton Landmarks in Mathema; Annals of Mathematics Studies; Princeton Landmarks in Mathematics and Physics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; MATHEMATICS / Number Theory, Number Theory