伽罗瓦理论 英文版PDF电子书下载

Symmetry 1

Rings 7

Domains and Fields 13

Homomorphisms and Ideals 17

Quotient Rings 21

Polynomial Rings over Fields 24

Prime Ideals and Maximal Ideals 31

Irreducible Polynomials 38

Classical Formulas 44

Splitting Fields 50

The Galois Group 59

Roots of Unity 63

Solvability by Radicals 71

Independence of Characters 76

Galois Extensions 79

The Fundamental Theorem of Galois Theory 83

Applications 85

Galois's Great Theorem 90

Discriminants 95

Galois Groups of Quadratics,Cubics,and Quartics 100

Epilogue 107

Appendix A:Group Theory Dictionary 109

Appendix B:Group Theory Used in the Text 112

Appendix C:Ruler-Compass Constructions 129

Appendix D:Old-fashioned Galois Theory 138

References 151

Index 153