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.
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.
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