具体描述
《代数》(第3版)：As I see it, the graduate course in algebra must primarily prepare studentsto handle the algebra which they will meet in all of mathematics: topology,partial differential equations, differential geometry, algebraic geometry, analysis,and representation theory, not to speak of algebra itself and algebraic numbertheory with all its ramifications. Hence I have inserted throughout references topapers and books which have appeared during the last decades, to indicate someof the directions in which the algebraic foundations provided by this book areused; I have accompanied these references with some motivating comments, toexplain how the topics of the present book fit into the mathematics that is tocome subsequently in various fields; and I have also mentioned some unsolvedproblems of mathematics in algebra and number theory. The abc conjecture isperhaps the most spectacular of these.
作者简介
Serge Lang (May 19, 1927–September 12, 2005) was a French-born American mathematician. He was known for his work in number theory and for his mathematics textbooks, including the influential Algebra. He was a member of the Bourbaki group.
He was born in Paris in 1927, and moved with his family to California as a teenager. He graduated from CalTech in 1946, and received a doctorate from Princeton University in 1951. He had positions at the University of Chicago and Columbia University (from 1955, leaving 1971 in a dispute). At the time of his death he was professor emeritus of mathematics at Yale University.
(From wikipedia.org)
目录信息
Chapter 1 Groups
1. Monoids
2. Groups
3. Normal subgroups
4. Cyclic groups
5. Operations of a group on a set
6. Sylow subgroups
7. Direct sums and free abelian groups
8. Finitely generated abelian groups
9. The dual group
10. Inverse limit and completion
11. Categories and functors
12. Free groups
Chapter 2 Rings
1. Rings and homomorphisms
2. Commutative rings
3. Polynomials and group rings
4. Localization
5. Principal and factorial rings
Chapter 3 Modules
Chapter 4 Polynomlals
Part Two Algebraic Equations
Chapter 5 Algebralc Extensions
Chapter 6 Galois Theory
Chapter 7 Extensions of Rings
Chapter 8 Transcendental Extensions
Chapter 9 Algebraic Spaces
Chapter 10 Noetherial Rings and Modules
Chapter 11 Real Fields
Chapter 12 Absolute Values
Part Three Liear Alebar and Reqresentations
Chapter 13 Matrices and Linear Maps
Chapter 14 Representatlon of One Endomorphism
Chapter 15 Structure of Bilinear Forms
Chapter 16 The Tensor Product
Chapter 17 Smisimplicity
Chapter 18 Representations of Finite Groups
Chapter 19 The Alternating Product
Part Four Homological Algebra
Chapter 20 General Homology Theory
Chapter 21 Finite Free Resolutions
Appendix 1 The Transcendence of e and
Appendix 2 Some Set Theory
Bibliography
Index
· · · · · · (收起)
读后感
习题答案讨论交流见http://tieba.baidu.com/p/3744612453 习题答案讨论交流见http://tieba.baidu.com/p/3744612453 习题答案讨论交流见http://tieba.baidu.com/p/3744612453
评分有幸David S. Dummit的儿子（Evan）给我上过algebra的补习班，他立荐的自然是他爸的书。就易读程度而言，Dummit, Foote可说是代数教程里数一数二的。内容涵盖了基本的代数所必用的知识，而且深入浅出，多有例举，即便是初学也可以读个八九不离十。 但这篇是评Lang的。Lang的书...
评分有幸David S. Dummit的儿子（Evan）给我上过algebra的补习班，他立荐的自然是他爸的书。就易读程度而言，Dummit, Foote可说是代数教程里数一数二的。内容涵盖了基本的代数所必用的知识，而且深入浅出，多有例举，即便是初学也可以读个八九不离十。 但这篇是评Lang的。Lang的书...
评分习题答案讨论交流见http://tieba.baidu.com/p/3744612453 习题答案讨论交流见http://tieba.baidu.com/p/3744612453 习题答案讨论交流见http://tieba.baidu.com/p/3744612453
评分有幸David S. Dummit的儿子（Evan）给我上过algebra的补习班，他立荐的自然是他爸的书。就易读程度而言，Dummit, Foote可说是代数教程里数一数二的。内容涵盖了基本的代数所必用的知识，而且深入浅出，多有例举，即便是初学也可以读个八九不离十。 但这篇是评Lang的。Lang的书...
用户评价
900多页书仅仅介绍了一个结构：模（表示是其同义词，群环域向量空间是其特例），一个结构定理模的分解为单模（表示分解为不可约表示），分解可以理解为非交换傅里叶变换（级数）；一个对偶Frobenius–Schur （伽瓦罗理论作为其特例）理解为傅里叶逆变换。连续和离散之间的类比关系是数学学科之间最大联系。希尔伯特基定理源自主理想环上模的定理和自同态分解jordan形式和有限生成交换群的结构定理等价。抽象代数的本质就是多项式，类比于调和分析本质把所有问题化归为了调和问题一样，抽象代数把所有的对象翻译为多项式，然后在多项式范畴里进行具体的思考。群表示就是非交换的傅里叶变换，庞特里亚金对偶的是局部紧群中的关键定理数学有时候初始学习的特例不好理解，例如伽瓦罗定理和傅里叶分析，但是把他们放在更加抽象的框架
评分就为了appendix那个精彩到high的Bourbaki theorem就已经算名著了。
评分就为了appendix那个精彩到high的Bourbaki theorem就已经算名著了。
评分如果你一直读的国产教程，如果你一直读的美国教程，那么这本法国教程你值得拥有。 它体现了布尔巴基学派的风格，不论你认同与否，都绝对值得你花时间去看看布尔巴基德风格。
评分只能看懂前几章，习题大多不会做
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