伽罗瓦对应导论
2011-7
世界图书出版公司
芬威克
235
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埃瓦里斯特·伽罗华是法国对函数论、方程式论和数论作出重要贡献的数学家，他的工作为群论奠定了基础；在父亲自杀后，他放弃投身于数学生涯，注册担任辅导教师，结果因撰写反君主制的文章而被开除，且因信仰共和体制而两次下狱。伽罗华死于一次近乎自杀的决斗，引起了后人的种种猜测。可能是被保皇派或警探所激怒而致，时年21岁。他被公认为是数学史上两个最具浪漫主义色彩的人物之一。
这本《伽罗瓦对应导论(第2版)》是英文版。
Preface
Chapter I.Preliminaries-Groups and Rings
1. Introduction to Groups
2. Quotient Groups and Sylow Subgroups
3. Finite Abelian Groups and Solvable Groups
4. Introduction to Rings
5. Factoring in F[x]
Chapter II. Field Exteio
1. Simple Exteio
2. Algebraic Exteio
3. Splitting Fields and Normal Exteio
Chapter III. The Galois Correspondence
1. The Fundamental Correspondence
2. The Solvable Correspondence
Chapter IV. Applicatio
1. Cotructibility
2. Roots of Unity
3. Wedderburn's Theorem
3. Dirichlet's Theorem and Finite Abelian Groups
Appendix A - Groups
1. Group Actio and the Sylow Theorems
2. Free Groups, Generato and Relatio
Appendix B - Factoring in Integral Domai
1. Euclidean Domai and Principal Ideal Domai
2. Prime and Irreducible Elements
3. Unique Factorization Domai
Appendix C - Vector Spaces
1. Subspaces, Linear Independence and Spanning
2. Bases and Dimeion
Bibliogr
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