Field Theory

  • Authors
  • 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. Pages 1-20
  3. Field Extensions

    1. Front Matter
      Pages 21-21
    2. Pages 23-40
    3. Pages 41-71
    4. Pages 93-109
  4. Galois Theory

  5. The Theory of Binomials

    1. Front Matter
      Pages 287-287
    2. Pages 289-308
    3. Pages 309-317
  6. Back Matter
    Pages 319-332

About this book


This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity.

For this new edition, the author has rewritten the text based on his experiences teaching from the first edition. There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities.

From the reviews of the first edition:

The book is written in a clear and explanatory style...the book is recommended for a graduate course in field theory as well as for independent study.

- T. Albu, Mathematical Reviews

...[the author] does an excellent job of stressing the key ideas. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study.

- J.N.Mordeson, Zentralblatt


Irreducibility Vector space algebra binomial finite field

Bibliographic information