代数

出版时间：2004-11  出版社：世界图书出版公司  作者：SERGE LANG  页数：914  
Tag标签：无  

内容概要

　　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.

书籍目录

Part One The Basic Objects of Algebra Chapter 1 Groups 1. Monoids 2. Groups 3. Normal subgroups 4. Cyclic groups5. 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 Rings1. Rings and homomorphisms 2. Commutative rings 3. Polynomials and group rings 4. Localization 5. Principal and factorial ringsChapter 3 ModulesChapter 4 PolynomlalsPart Two Algebraic EquationsChapter 5 Algebralc ExtensionsChapter 6 Galois TheoryChapter 7 Extensions of RingsChapter 8 Transcendental ExtensionsChapter 9 Algebraic SpacesChapter 10 Noetherial Rings and ModulesChapter 11 Real FieldsChapter 12 Absolute ValuesPart Three Liear Alebar and ReqresentationsChapter 13 Matrices and Linear MapsChapter 14 Representatlon of One EndomorphismChapter 15 Structure of Bilinear FormsChapter 16 The Tensor ProductChapter 17 SmisimplicityChapter 18 Representations of Finite GroupsChapter 19 The Alternating ProductPart Four Homological AlgebraChapter 20 General Homology TheoryChapter 21 Finite Free ResolutionsAppendix 1 The Transcendence of e and Appendix 2 Some Set TheoryBibliographyIndex

用户评论 (总计15条)

•   好多人觉得lang的书乱写，呵呵。本来写分析吧，结果扯好多代数；本来写代数吧，甚至几何都出来了初学者不喜欢是显然的。太综合了甚至有人说干巴晦涩可是如果有点基础，你会发现，lang真是了不起的大师。lang的书相当有启发。感觉乱的话，我猜可能你基础不够吧我已经读了好几本lang的书了，分析、几何、代数都有。数学本就一体，拆成孤立的分支，写成一本本课本，其实是方便“教学”不得已而为之罢了。
•   非常好的一本代数书，可以称之为代数学的一本字典，覆盖了代数的很多方面。
•   After having struggled with this book for most of my first year algebra class I grew to hate it! I now find myself refering to this book time and time again. This book really has it all. If you already have a good background in algebra and want a great referance, this book is a must. If you are taking algebra for the first time I would avoid this book and look at another intro. to algebra text like Grove (one of my favorite math texts).
•   Serge Lang的这本书是一本经典。本书的最大特点就是写得很抽象，同时处理得很干净。全书没有一句废话，每个例子都有鲜明的特点，是一本极好的代数书。对本科生而言可以与Lang的undergraduate algebra一起看。
•   内容很多很详细，研究生的课本，也适合本科生读
•   帮同学代买的，不错，第二天就到了，因为忙于考试，一直没空来评价，必须卓越！必须给力！
•   很好的SL书籍，研究生参考教材
•   印刷很不错，很清晰。就是这么大部头又是硬壳的，翻起来不是很方便，怕弄坏。
•   这本书 不愧为代数学大辞典，非常全面细致
•   内容很丰富，个人觉得作为工具书将会更好！
•   这本书是我最喜欢的两本代数书之一，书中的定理和例子很不错！
•   经典教材，不过不适合初学者。。
•   神作 但是听说 第二版比第三版好？》
•   简单的来说，只需看三页，你就知道这是一本无法代替的书。事实上，这本书之后，除了Artin的那本《代数》，没有书超过这本的框架。这是Artin的书中译本扉页上写的，所言不虚。这是第三版，绝对值得拥有。
•   塞尔日·兰的经典教材，里面的证明还是很好懂的。可惜是Hardcover线装书，用久了书会变厚。