《伽羅瓦對應導論（第2版）》是2011年世界圖書出版公司出版的著作，作者是[美] 芬威克。
基本介紹
- 書名：《伽羅瓦對應導論（第2版）》
- 作者：[美] 芬威克
- 出版社：世界圖書出版公司
- 出版時間：2011-07-01
內容簡介,目錄,
內容簡介
《伽羅瓦對應導論（第2版）》是一部比較獨立的教程，具有基本數學背景的讀者即可學習《伽羅瓦對應導論（第2版）》。導引部分包括Sylow p-子群、可解群和有限群和abelian 群的結構，這些都為學習伽羅瓦對應提供了堅實的基礎。
目錄
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 Extensions
1. Simple Extensions
2. Algebraic Extensions
3. Splitting Fields and Normal Extensions
Chapter Ⅲ The Galois Correspondence.
1. The Fundamental Correspondence
2. The Solvable Correspondence
Chapter Ⅳ Applications
1. Constructibility
2. Roots of Unity
3. Wedderburn's Theorem
3. Dirichlet's Theorem and Finite Abelian Groups
Appendix A-Groups
1. Group Actions and the Sylow Theorems
2. Free Groups, Generators and Relations
Appendix B-Factoring in Integral Domains
1. Euclidean Domains and Principal Ideal Domains
2. Prime and Irreducible Elements
3. Unique Factorization Domains
Appendix C-Vector Spaces
1. Subspaces, Linear Independence and Spanning
2. Bases and Dimension
Bibliography
Index
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 Extensions
1. Simple Extensions
2. Algebraic Extensions
3. Splitting Fields and Normal Extensions
Chapter Ⅲ The Galois Correspondence.
1. The Fundamental Correspondence
2. The Solvable Correspondence
Chapter Ⅳ Applications
1. Constructibility
2. Roots of Unity
3. Wedderburn's Theorem
3. Dirichlet's Theorem and Finite Abelian Groups
Appendix A-Groups
1. Group Actions and the Sylow Theorems
2. Free Groups, Generators and Relations
Appendix B-Factoring in Integral Domains
1. Euclidean Domains and Principal Ideal Domains
2. Prime and Irreducible Elements
3. Unique Factorization Domains
Appendix C-Vector Spaces
1. Subspaces, Linear Independence and Spanning
2. Bases and Dimension
Bibliography
Index
