Skip to main content
SpringerLink
Log in

Lectures in Abstract Algebra

III. Theory of Fields and Galois Theory

  • Textbook
  • © 1964

Overview

Authors:
  1. Nathan Jacobson

    1. Department of Mathematics, Yale University, New Haven, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (7 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Introduction

    • Nathan Jacobson
    Pages 1-17

  3. Finite Dimensional Extension Fields

    • Nathan Jacobson
    Pages 18-88

  4. Galois Theory of Equations

    • Nathan Jacobson
    Pages 89-109

  5. Abelian Extensions

    • Nathan Jacobson
    Pages 110-140

  6. Structure Theory of Fields

    • Nathan Jacobson
    Pages 141-209

  7. Valuation Theory

    • Nathan Jacobson
    Pages 210-268

  8. Artin-Schreier Theory

    • Nathan Jacobson
    Pages 269-318

  9. Back Matter

    Pages 319-323
    Download chapter PDF
Back to top

Keywords

About this book

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 ofinterest 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.

Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    Nathan Jacobson

Bibliographic Information

  • Book Title: Lectures in Abstract Algebra

  • Book Subtitle: III. Theory of Fields and Galois Theory

  • Authors: Nathan Jacobson

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-9872-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media, LLC 1964

  • Softcover ISBN: 978-0-387-90124-4Published: 01 January 1964

  • eBook ISBN: 978-1-4612-9872-4Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XII, 324

  • Additional Information: Originally published by Van Nostrand, Princeton, NJ, 1964

  • Topics: Algebra

Publish with us

Policies and ethics

Back to top

Search

Navigation