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Field Theory

  • Steven┬áRoman

Part of the Graduate Texts in Mathematics book series (GTM, volume 158)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Preliminaries

    1. Steven Roman
      Pages 1-21
  3. Basic Theory

    1. Front Matter
      Pages 23-23
    2. Steven Roman
      Pages 25-38
    3. Steven Roman
      Pages 39-59
    4. Steven Roman
      Pages 61-77
    5. Steven Roman
      Pages 79-98
  4. Galois Theory

    1. Front Matter
      Pages 99-99
    2. Steven Roman
      Pages 101-126
    3. Steven Roman
      Pages 127-145
    4. Steven Roman
      Pages 147-160
    5. Steven Roman
      Pages 161-174
    6. Steven Roman
      Pages 175-185
  5. The Theory of Binomials

    1. Front Matter
      Pages 187-187
    2. Steven Roman
      Pages 189-208
    3. Steven Roman
      Pages 209-214
    4. Steven Roman
      Pages 215-225
    5. Steven Roman
      Pages 227-246
    6. Steven Roman
      Pages 247-255
  6. Back Matter
    Pages 257-274

About this book

Introduction

Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials - the Kummer theory.

Keywords

Galois theory Irreducibility binomial field theory of fields

Authors and affiliations

  • Steven┬áRoman
    • 1
  1. 1.Department of MathematicsCalifornia State UniversityFullertonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-2516-4
  • Copyright Information Steven Roman 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94408-1
  • Online ISBN 978-1-4612-2516-4
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site