| INTRODUCTION SECTION 1. Extension of homomorphisms 2. Algebras 3. Tensor products of vector spaces 4. Tensor product of algebras CHAPTER I￡oFINITE DIMENSIONAL EXTENSION FIELDS 1. Some vector spaces associated with mappings of fields 2. The Jacobson-Bourbaki correspondence 3. Dedekind independence theorem for isomorphisms of a field 4. Finite groups of automorphisms 5. Splitting field of a polynomial 6. Multiple roots. Separable polynomials 7. The “fundamental theorem” of Galois theory 8. Normal extensions. Normal closures 9. Structure of algebraic extensions. Separability 10. Degrees of separability and inseparability. Structure of normal extensions 11. Primitive elements 12. Normal bases 13. Finite fields 14. Regular representation， trace and norm 15. Galois cohomology 16. Composites of fields CHAPTER II￡oGALOIS THEORY OF EQUATIONS 1. The Galois group of an equation 2. Pure equations 3. Galois' criterion for solvability by radicals …… |
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