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Theory of Commutative Fields
 
Masayoshi Nagata Kyoto University, Kyoto, Japan
Front Cover for Theory of Commutative Fields
Available Formats:
Electronic ISBN: 978-1-4704-4533-1
Product Code: MMONO/125.E
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Front Cover for Theory of Commutative Fields
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  • Front Cover for Theory of Commutative Fields
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Theory of Commutative Fields
Masayoshi Nagata Kyoto University, Kyoto, Japan
Available Formats:
Electronic ISBN:  978-1-4704-4533-1
Product Code:  MMONO/125.E
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 1251993; 249 pp
    MSC: Primary 12;

    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.

  • Table of Contents
     
     
    • Chapters
    • Chapter 0. Prerequisites from set theory
    • Chapter I. Groups, rings, and fields
    • Chapter II. Algebraic extensions of finite degrees
    • Chapter III. Transcendental extensions
    • Chapter IV. Valuations
    • Chapter V. Formally real fields
    • Chapter VI. Galois theory of algebraic extensions of infinite degree
  • Reviews
     
     
    • 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
  • Request Review Copy
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Volume: 1251993; 249 pp
MSC: Primary 12;

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.

  • Chapters
  • Chapter 0. Prerequisites from set theory
  • Chapter I. Groups, rings, and fields
  • Chapter II. Algebraic extensions of finite degrees
  • Chapter III. Transcendental extensions
  • Chapter IV. Valuations
  • Chapter V. Formally real fields
  • Chapter VI. Galois theory of algebraic extensions of infinite degree
  • 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
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