Lectures in Abstract Algebra

III. Theory of Fields and Galois Theory

  • Nathan Jacobson

Part of the Graduate Texts in Mathematics book series (GTM, volume 32)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Nathan Jacobson
    Pages 1-17
  3. Nathan Jacobson
    Pages 18-88
  4. Nathan Jacobson
    Pages 89-109
  5. Nathan Jacobson
    Pages 110-140
  6. Nathan Jacobson
    Pages 141-209
  7. Nathan Jacobson
    Pages 210-268
  8. Nathan Jacobson
    Pages 269-318
  9. Back Matter
    Pages 319-323

About this book

Introduction

The present volume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we give here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume, dealing with linear algebra. The level of the present work is roughly the same as that of Volume II. In preparing this book we have had a number of objectives in mind. First and foremost has been that of presenting the basic field theory which is essential for an understanding of modern algebraic number theory, ring theory, and algebraic geometry. The parts of the book concerned with this aspect of the subject are Chapters I, IV, and V dealing respectively with finite dimen­ sional field extensions and Galois theory, general structure theory of fields, and valuation theory. Also the results of Chapter IlIon abelian extensions, although of a somewhat specialized nature, are of interest in number theory. A second objective of our ac­ count has been to indicate the links between the present theory of fields and the classical problems which led to its development.

Keywords

Abstract algebra Algebraic curve Finite Galois theory Morphism Vector space algebra commutative group equation function geometry homomorphism ring theory theorem theory of fields

Authors and affiliations

  • Nathan Jacobson
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-9872-4
  • Copyright Information Springer-Verlag New York 1964
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90124-4
  • Online ISBN 978-1-4612-9872-4
  • Series Print ISSN 0072-5285
  • About this book