ProofWiki:Books/Iain T. Adamson/Introduction to Field Theory

Iain T. Adamson: Introduction to Field Theory

Published 1964, Oliver & Boyd.

Subject Matter

• Field Theory
• Galois Theory

Contents

PREFACE

CHAPTER I: ELEMENTARY DEFINITIONS

1. Rings and fields

2. Elementary properties

3. Homomorphisms

4. Vector spaces

5. Polynomials

6. Higher polynomial rings; rational functions

Examples I

CHAPTER 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

Examples II

CHAPTER 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

Examples III

CHAPTER IV: APPLICATIONS

20. Finite fields

21. Cyclotomic extensions

22. Cyclotomic extensions of the rational number field

23. Cyclic extensions

24. Wedderburn's theorem

25. Ruler-and-compasses constructions

26. Solution by radicals

27. Generic polynomials

Examples IV

READING LIST

INDEX OF NOTATIONS

INDEX