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Introduction to Field Theory

Introduction to Field Theory

2nd Edition

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

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  • 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

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    Product details

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

    Preface
    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

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