The theory of classical valuations
By: Paulo Ribenboim.
Publisher: Springer
Published: 1999
Place of publication: New York
Language: eng
Number of pages: 403
Subjects: Algebraic fields; Valuation theory
Description: In the second half of the last century, Kummer introduced "local" methods in his study of Fermat's last theorem. Hensel constructed the p-adic numbers and proved the so-called "Hensel lemma." Kurschak formally introduced the concept of a valuation of a field, and Ostrowski, Hasse, Schmidt, Krull, and others developed the theory. These classical valuations play a central cental role in the study of number fields and algebraic functions of one variable.

The present book is one of the first texts in English devoted to the beautiful theory of classical valuations. The book is self-contained and up-to-date, and proofs are given in full detail. Thus, it will be an invaluable resource for graduate students and research mathematicians.
Notes: Includes bibliographical references (p. 391-393) and index.