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
Source work progress
- 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 4$. Vector Spaces: Theorem $4.2$