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Theory of Commutative Fields
Masayoshi Nagata, Kyoto University, Japan

Translations of Mathematical Monographs
1993; 249 pp; hardcover
Volume: 125
ISBN-10: 0-8218-4572-1
ISBN-13: 978-0-8218-4572-1
List Price: US$110
Member Price: US$88
Order Code: MMONO/125
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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.


Graduate students and research mathematicians.


"The book ... gives an interesting and very clear introduction to commutative algebra."

-- Mathematical Reviews

"Very much self-contained."

-- 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
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