Skip to content
Register Sign in Wishlist
Introduction to Field Theory

Introduction to Field Theory

2nd Edition

  • Date Published: September 1982
  • availability: Available
  • format: Paperback
  • isbn: 9780521286589


Add to wishlist

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • Field Theory is a fascinating branch of algebra, with many interesting applications, and its central result, the Fundamental Theorem of Galois Theory, is by any standards one of the really important theorems of mathematics. This book brings the reader from the basic definitions to important results and applications, and introduces him to the spirit and some of the techniques of abstract algebra. It is addressed to undergraduates in pure mathematics and presupposes only a little knowledge of elementary group theory. Chapter I develops the elementary properties of rings and fields including the notions of characteristic, prime fields and various types of homomorphisms. In Chapter II extension fields and various ways of classifying them are studies. Chapter III gives an exposition of the Galois Theory, following Artin's approach, and Chapter IV provides a wide variety of applications of the preceding theory. For the second edition Dr Adamson has improved the exposition in places, made corrections and updated the references.

    Reviews & endorsements

    Review of the hardback: 'This is an attractive book on field theory and Galois theory…it is very clearly written, with many examples, and the exercises are good…an excellent introduction.' American Mathematical Monthly

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Edition: 2nd Edition
    • Date Published: September 1982
    • format: Paperback
    • isbn: 9780521286589
    • length: 192 pages
    • dimensions: 203 x 127 x 11 mm
    • weight: 0.22kg
    • availability: Available
  • Table of Contents

    Part I: Elementary Definitions
    1. Rings and fields
    2. Elementary properties
    3. Homomorphisms
    4. Vector spaces
    5. Polynomials
    6. Higher polynomial rings
    rational functions
    Part II: Extensions of fields
    7. Elementary properties
    8. Simple extensions
    9. Algebraic extensions
    10. Factorisation of polynomials
    11. Splitting fields
    12. Algebraically closed fields
    13. Separable extensions
    Part III: Galois theory
    14. Automorphisms of fields
    15. Normal extensions
    16. The fundamental theorem of Galois Theory
    17. Norms and traces
    18. The primitive element theorem
    Lagrange's theorem
    19. Normal bases
    Part IV: Applications
    20. Finite fields
    21. Cyclotomic extensions
    22. Cyclotomic extensions of the rational number field
    23. Cyclic extensions
    24. Wedderburns' theorem
    25. Ruler-an-compasses constructions
    26. Solution by radicals
    27. Generic polynomials.

  • Author

    Iain T. Adamson

Related Books

also by this author

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.