域和伽罗瓦理论(英文版)9787506259552
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作者P.Morandi|责编:刘慧//高蓉
出版社世界图书出版公司
ISBN9787506259552
出版时间2003-08
装帧平装
开本其他
定价69元
货号30934958
上书时间2024-07-28
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目录
Preface
Notes to the Reader
List of Symbols
Ⅰ Galois Theory
1 Field Extensions
2 Automorphisms
3 Normal Extensions
4 Separable and Inseparable Extensions
5 The Fundamental Theorem of Galois Theory
Ⅱ Some Galois Extensions
6 Finite Fields
7 Cyclotomic Extensions
8 Norms and Traces
9 Cyclic Extensions
10 Hilbert Theorem 90 and Group Cohomology.
11 Kummer Extensions
Ⅲ Applications of Galois Theory
12 Discriminants
13 Polynomials of Degree 3 and 4
14 The Transcendence of 7r and e
15 Ruler and Compass Constructions
16 Solvability by Radicals
Ⅳ Infinite Algebraic Extensions
17 Infinite Galois Extensions
18 Some Infinite Galois Extensions
Ⅴ Transcendental Extensions
19 Transcendence Bases
20 Linear Disjointness
21 Algebraic Varieties
22 Algebraic Function Fields
23 Derivations and Differentials
Appendix A Ring Theory
1 Prime and Maximal Ideals
2 Unique Factorization Domains
3 Polynomials over a Field
4 Factorization in Polynomial Rings
5 Irreducibility Tests
Appendix B Set Theory
1 Zorn's Lemma
2 Cardinality and Cardinal Arithmetic
Appendix C Group Theory
1 Fundamentals of Finite Groups
2 The Sylow Theorems
3 Solvable Groups
4 Profinite Groups
Appendix D Vector Spaces
1 Bases and Dimension
2 Linear Transformations
3 Systems of Linear Equations and Determinants
4 Tensor Products
Appendix E Topology
1 Topological Spaces
2 Topological Properties
References
Index
内容摘要
域是有理数集合、实数集合、复数集合的抽象模型，因此在整个数学科学中处于基础地位。Galois是最早提出有限域观点的人，他对于抽象域理论的诞生至关重要 本书把抽象域论一分为二，首先讲代数扩张及其在代数域论上的应用，其次介绍超越扩张及其在代数函数论及代数几何上的应用，中间还插入经典的Galois理论，使读者对于实际背景有比较清楚的认识。
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