具體描述
《代數》(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.
著者簡介
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)
圖書目錄
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)
讀後感
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...
評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
評分有幸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...
評分有幸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...
評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
用戶評價
就為瞭appendix那個精彩到high的Bourbaki theorem就已經算名著瞭。
评分就為瞭appendix那個精彩到high的Bourbaki theorem就已經算名著瞭。
评分隻能看懂前幾章，習題大多不會做
评分如果你一直讀的國産教程，如果你一直讀的美國教程，那麼這本法國教程你值得擁有。 它體現瞭布爾巴基學派的風格，不論你認同與否，都絕對值得你花時間去看看布爾巴基德風格。
评分隻能看懂前幾章，習題大多不會做
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