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Field Theory

  • Textbook
  • © 1995

Overview

Authors:
  1. Steven Roman

    1. Department of Mathematics, California State University, Fullerton, USA

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

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xii
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  2. Preliminaries

    1. Preliminaries

      • Steven Roman
      Pages 1-21

  3. Basic Theory

    1. Front Matter

      Pages 23-23
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    2. Polynomials

      • Steven Roman
      Pages 25-38

    3. Field Extensions

      • Steven Roman
      Pages 39-59

    4. Algebraic Independence

      • Steven Roman
      Pages 61-77

    5. Separability

      • Steven Roman
      Pages 79-98

  4. Galois Theory

    1. Front Matter

      Pages 99-99
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    2. Galois Theory I

      • Steven Roman
      Pages 101-126

    3. Galois Theory II

      • Steven Roman
      Pages 127-145

    4. A Field Extension as a Vector Space

      • Steven Roman
      Pages 147-160

    5. Finite Fields I: Basic Properties

      • Steven Roman
      Pages 161-174

    6. Finite Fields II: Additional Properties

      • Steven Roman
      Pages 175-185

  5. The Theory of Binomials

    1. Front Matter

      Pages 187-187
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    2. The Roots of Unity

      • Steven Roman
      Pages 189-208

    3. Cyclic Extensions

      • Steven Roman
      Pages 209-214

    4. Solvable Extensions

      • Steven Roman
      Pages 215-225

    5. Binomials

      • Steven Roman
      Pages 227-246

    6. Families of Binomials

      • Steven Roman
      Pages 247-255

  6. Back Matter

    Pages 257-274
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, California State University, Fullerton, USA

    Steven Roman

Bibliographic Information

  • Book Title: Field Theory

  • Authors: Steven Roman

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-2516-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Steven Roman 1995

  • eBook ISBN: 978-1-4612-2516-4Published: 20 December 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: 292

  • Topics: Algebra, Number Theory

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