Book:Iain T. Adamson/Introduction to Field Theory

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Iain T. Adamson: Introduction to Field Theory

Published $\text {1964}$, Oliver & Boyd.


Subject Matter


Contents

Preface
CHAPTER $\text {I}$: ELEMENTARY DEFINITIONS
1. Rings and fields
2. Elementary properties
3. Homomorphisms
4. Vector spaces
5. Polynomials
6. Higher polynomial rings; rational functions
Examples $\text {I}$
CHAPTER $\text {II}$: 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 $\text {II}$
CHAPTER $\text {III}$: 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 $\text {III}$
CHAPTER $\text {IV}$: 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 $\text {IV}$
Reading List
Index of Notations
Index


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