伽罗瓦理论 英文版PDF电子书下载

本书用完整的证明和大量练习清晰、有效地讲述了Galois理论。包括：立方、四次方公式的Galois理论的基本理论；五次Galois大定理的不可解性；立方和四次方Galois群的计算。补充了群论、尺规结构和Galois的早期历史。本书是一本Galois理论简明教程，很适合研究生一年级作为教材学习；也是一本很理想的课外学习书。

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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

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