Translations of Mathematical Monographs 1993; 249 pp; hardcover Volume: 125 ISBN10: 0821845721 ISBN13: 9780821845721 List Price: US$110 Member Price: US$88 Order Code: MMONO/125
 The theory of commutative fields is a fundamental area of mathematics, particularly in number theory, algebra, and algebraic geometry. However, few books provide sufficient treatment of this topic. This book is a translation of the 1985 updated edition of Nagata's 1967 book; both editions originally appeared in Japanese. Nagata provides an introduction to commutative fields that is useful to those studying the topic for the first time as well as to those wishing a reference book. The book presents, with as few prerequisites as possible, all of the important and fundamental results on commutative fields. Each chapter ends with exercises, making the book suitable as a textbook for graduate courses or for independent study. Readership Graduate students and research mathematicians. Reviews "The book ... gives an interesting and very clear introduction to commutative algebra."  Mathematical Reviews "Very much selfcontained."  Zentralblatt MATH "Students wanting a thorough introduction into field theory will profit by reading it, all the more as a bunch of exercises is added together with answers and hints."  Monatshefte für Mathematik Table of Contents  Prerequisites from set theory
 Groups, rings, and fields
 Algebraic extensions of finite degrees
 Transcendental extensions
 Valuations
 Formally real fields
 Galois theory of algebraic extensions of infinite degree
 Answers and hints
 Index of symbols
 Subject index
