Book:Iain T. Adamson/Introduction to Field Theory

From ProofWiki
Jump to: navigation, search

Iain T. Adamson: Introduction to Field Theory

Published $1964$, Oliver & Boyd.


Subject Matter


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