同调代数

出版时间：2011-7  出版社：世界图书出版公司  作者：嘉当  页数：390  
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内容概要

　　本书是数学发展史上的一个里程碑，在很长一段时间，这是唯一本讲述拓扑代数的教程。这本书堪称是一部同调代数经典，1956年初版，至今已有七次重印出版。这本书曾在纯代数领域引起过不小的轰动，作者企图将这个领域统一起来，并且为这个领域构建一个完整的框架。书中讲述的同调理论包含了群、李代数和结合代数上同调结构，大量的结果都包括在一般框架之中，但每个结果都有不同的讲述方式，并且每个理论的特殊性质都给出了具体的讲述。本书以环上的模作为出发点，基本计算有二模张量积，以及一个模到其他模的全部同态群。函子和导出函子也是自然而然的进行了讲述。目次：环和模；加性函数；卫星；同调；导出函子；u和hom的导出函子；积分域；增广环；结合代数；补充代数；乘积；有限群；李代数；扩张；谱序列；谱序列应用；超拓扑。
　　读者报对象：数学、代数拓扑专业的的学生，教师及相关专业的读者。

作者简介

作者：(法国)嘉当 (Henri Cartan)

书籍目录

preface
chapter i. rings and modules
　1. preliminaries
　2. projective modules
　3. injective modules
　4. semi-simple rings
　5. hereditary rings
　6. semi-hereditary rings
　7. noetherian tings
　　exercises
chapter ii. additive functors
　1. definitions
　2. examples
　3. operators
　4. preservation of exactness
　5. composite functors
　6. change of rings
　　exercises
chapter iii. satellites
　1. definition of satellites
　2. connecting homomorphisms
　3. half exact functors
　4. connected sequence of functors
　5. axiomatic description of satellites
　6. composite functors
　7. several variables
　　exercises
chapter iv. homology
　1. modules with differentiation
　2. the ring of dual numbers
　3. graded modules, complexes
　4. double gradings and complexes
　5. functors of complexes
　6. the homomorphism
　7. the homomorphism a (continuation)
　8. kiinneth relations
　　exercises
chapter v. derived functors
　1. complexes over modules; resolutions
　2. resolutions of sequences
　3. definition of derived functors
　4. connecting homomorphisms
　5. the functors rot and lot
　6. comparison with satellites
　7. computational devices
　8. partial derived functors
　9. sums, products, limits
　i0. the sequence of a map
　　exercises
chapter vi. derived functors of ~ and hem
　1. the functors tor and ext
　2. dimension of modules and rings
　3. kiinneth relations
　4. change of rings
　5. duality homomorphisms
　　exercises
chapter vli. integral domains
　1. generalities
　2. the field of quotients
　3. inversible ideals
　4. priifer rings
　5. dedekind rings
　6. abelian groups
　7. a description of torx (a,c)
　　exercises
chapter viii. augmented rings
　1. homology and cohomology of an augmented ring
　2. examples
　3. change of rings
　4. dimension
　5. faithful systems
　6. applications to graded and local rings
　　exercises
chapter ix. associative algebras
　1. algebras and their tensor products
　2. associativity formulae
　3. the enveloping algebra a~
　4. homology and cohomology of algebras
　5. the hochschild groups as functors of a
　6. standard complexes
　7. dimension
　　exercises
chapter x. supplemented algebras
　1. homology of supplemented algebras
　2. comparison with hochschild groups
　3. augmented monoids
　4. groups
　5. examples of resolutions
　6. the inverse process
　7. subalgebras and subgroups
　8. weakly injective and projective modules
　　exercises
chapter xi. products
　1. external products
　2. formal properties of the products
　3. lsomorphisms
　4. internal products
　5. computation of products
　6. products in the hochschild theory
　7. products for supplemented algebras
　8. associativity formulae
　9. reduction theorems
　　exercises
chapter xii. finite groups
　1. norms
　2. the complete derived sequence
　3. complete resolutions
　4. products for finite groups
　5. the uniqueness theorem
　6. duality
　7. examples
　8. relations with subgroups
　9. double cosets
　10. p-groups and sylow groups
　1. periodicity
　　exercises
chapter xlli. lie algebras
　1. lie algebras and their enveloping algebras
　2. homology and cohomology of lie algebras
　3. the poincare-witt theorem
　4. subaigebras and ideals
　5. the diagonal map and its applications
　6. a relation in the standard complex
　7. the complex v(g)
　8. applications of the complex v(g)
　　exercises
chapter xiv. extensions
　1. extensions of modules
　2. extensions of associative algebras
　3. extensions of supplemented algebras
　4. extensions of groups
　5. extensions of lie algebras
　　exercises
chapter xv. spectral sequences
　1. filtrations and spectral sequences
　2. convergence
　3. maps and homotopies
　4. the graded case
　5. induced homomorphisms and exact sequences
　6. application to double complexes
　7. a generalization
　　exercises
chapter xvi. applications of spectral sequences
　1. partial derived functors
　2. functors of complexes
　3. composite functors
　4. associativity formulae
　5. applications to the change of rings
　6. normal subalgebras
　7. associativity formulae using diagonal maps
　8. complexes over algebras
　9. topological applications
　10. the almost zero theory
　　exercises
chapter xvll. hyperhomology
　1. resolutions of complexes
　2. the invariants
　3. regularity conditions
　4. mapping theorems
　5. kiinneth relations
　6. balanced functors
　7. composite functors
appendix: exact categories, by david a. buchsbaum
list of symbols
index of terminology

章节摘录

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编辑推荐

《同调代数(英文)》：Rings and modules，additive functors，statllites等章节。

用户评论 (总计3条)

•   这本同调代数，比较偏重于他在拓扑中的应用
•   这本书huanhao
•   经典教材，内容详尽，很好很强大