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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 Click above image for expanded view 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.

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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.

• 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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