扫一扫
关注中图网
官方微博
本类五星书更多>
-
>
宇宙、量子和人类心灵
-
>
考研数学专题练1200题
-
>
希格斯:“上帝粒子”的发明与发现
-
>
神农架叠层石:10多亿年前远古海洋微生物建造的大堡礁
-
>
二十四史天文志校注(上中下)
-
>
声音简史
-
>
浪漫地理学:追寻崇高景观
Field and Galois Theory 版权信息
- ISBN：9787506259552
- 条形码：9787506259552 ; 978-7-5062-5955-2
- 装帧：平装
- 册数：暂无
- 重量：暂无
- 所属分类：>>
Field and Galois Theory 内容简介
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*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。
Field and Galois Theory 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
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
展开全部
书友推荐
- >
推拿
推拿
¥12.2¥32.0 - >
名家带你读鲁迅:朝花夕拾
名家带你读鲁迅:朝花夕拾
¥10.5¥21.0 - >
二体千字文
二体千字文
¥14.0¥40.0 - >
姑妈的宝刀
姑妈的宝刀
¥9.0¥30.0 - >
随园食单
随园食单
¥15.4¥48.0 - >
巴金－再思录
巴金－再思录
¥14.7¥46.0 - >
回忆爱玛侬
回忆爱玛侬
¥23.0¥32.8 - >
企鹅口袋书系列·伟大的思想20:论自然选择(英汉双语)
企鹅口袋书系列·伟大的思想20:论自然选择(英汉双语)
¥6.3¥14.0
本类畅销
-
怎样解题
¥17.2¥29 -
自然哲学的数学原理-拟定经典力学世界图景的旷世巨典-全新修订本
¥39.4¥58 -
数学-应用与思考
¥16.1¥32.8 -
数学万花筒 修订版
¥32.4¥49 -
数学万花筒-夏尔摩斯探案集-3
¥30.1¥39 -
新型元启发式算法及其应用
¥77.4¥98
