A Course in Galois theory /
From an elementary discussion of groups, fields and vector spaces, this introduction to Galois theory progresses to rings, extension fields, ruler-and-compass constructions, automorphisms and Galois correspondence. Publisher's note
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1986
Cambridge [Cambridgeshire] ; New York : 1986 |
| Subjects: |
Table of Contents:
- Machine derived contents note: Preface
- Part I. Algebraic Preliminaries: 1. Groups, fields and vector spaces
- 2. The axiom of choice, and Zorn's lemma
- 3. Rings
- Part II. The Theory of Fields, and Galois Theory: 4. Field extensions
- 5. Tests for irreducibility
- 6. Ruler-and-compass constructions
- 7. Splitting fields
- 8. The algebraic closure of a field
- 9. Normal extensions
- 10. Separability
- 11. Automorphisms and fixed fields
- 12. Finite fields
- 13. The theorem of the primative element
- 14. Cubics and quartics
- 15. Roots of unity
- 16. Cyclic extensions
- 17. Solution by radicals
- 18. Transcendental elements and algebraic independence
- 19. Some further topics
- 20. The calculation of Galois groups
- Index