- 域和伽罗瓦理论(英文版)
- - 作者：P.Morandi|责编:刘慧//高蓉
  - 出版社：世界图书出版公司
  - ISBN：9787506259552
  - 出版日期：2003/08/01
  - 页数：281
- 售价：27.6

内容大纲
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。
作者介绍
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

内容大纲

作者介绍

目录

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