Electronic ISBN:  9781470445331 
Product Code:  MMONO/125.E 
List Price:  $110.00 
MAA Member Price:  $99.00 
AMS Member Price:  $88.00 

Book DetailsTranslations of Mathematical MonographsVolume: 125; 1993; 249 ppMSC: 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.
ReadershipGraduate 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 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


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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.

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 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