作者：P.J.hilton,U.Stammba
页数：380
出版社：世界图书出版公司
出版日期：2003
ISBN：9787506260077
电子书格式：pdf/epub/txt
内容简介
本书是一本比较标准的同调代数教材，从60年代末开始在瑞士联邦理工学院及美国几所大学使用，第1版曾重印3次, 本版在第1版的基础上增加了新内容——同调代数的应用和新展。本书内容比较详细全面，基础理论十分扎实；论述也比较深入浅出，通俗易懂，有很好的例题和习题。本书第1版曾编为W1/4。目次：模；范畴与函子；模的扩张；导出函子；Kunneth公式；群的上同调；李代数的上同调；正合偶和谱序列；伴随性和同调论;应用和最新进展。
作者简介
P.J.Hilton，纽约州立大学宾汉姆顿分校(State University of New York Binghamton)数学系教授，A Course in Homological Algebra和Symposium on Algebraic Topology很受读者认可。
目录
Preface to the Second Edition
Introduction
Ⅰ.Modules
1.Modules
2.The Group of Homomorphisms
3.Sums and Products
4.Free and Projective Modules
5.Projective Modules over a Principal Ideal Domain
6.Dualization, Injective Modules
7.Injective Modules over a Principal Ideal Domain
8.Cofree Modules
9.Essential Extensions
Ⅱ.Categories and Functors
1.Categories
2.Functors
3.Duality
4.Natural Transformations
5.Products and Coproducts; Universal Constructions
6.Universal Constructions (Continued); Pull-backs and Push-outs
7.Adjoint Functors
8.Adjoint Functors and Universal Constructions
9.Abelian Categories
10.Projective, Injective, and Free Objects
Ⅲ.Extensions of Modules
1.Extensions
2.The Functor Ext
3.Ext Using Injectives
4.Computation of some Ext-Groups
5.Two Exact Sequences
6.A Theorem of Stein-Serre for Abelian Groups
7.The Tensor Product
8.The Functor Tor
Ⅳ.Derived Funetors
1.Complexes
2.The Long Exact (Co) Homology Sequence
3.Homotopy
4.Resolutions
5.Derived Functors
6.The Two Long Exact Sequences of Derived Functor
7.The Functors ExtnΛ Using Projectives
8.The Functors ExtnΛ Using Injectives
9.Extn and n-Extensions
10.Another Characterization bfDerived Functors
11.The Functor TotΛn
12.Change of Rings
Ⅴ.The Kunneth Formula
1.Double Complexes
2.The Kiinneth Theorem
3.The Dual Kunneth Theorem
4.Applications of the Kunneth Formulas
Ⅵ.Cohomology of Groups
1.The Group Ring
2.Definition of (Co) Homology
3.H0, H0
4.H1, H1 with Trivial Coefficient Modules
5.The Augmentation Ideal, Derivations, and the Semi-Direct Product
6.A Short Exact Sequence
7.The (Co) Homology of Finite Cyclic Groups
8.The 5-Term Exact Sequences
9.H2, Hopf’s Formula, and the Lower Central Series
10.H2 and Extensions
11.Relative Projeetives and Relative Injectives
12.Reduction Theorems
13.Resolutions
14.The (Co) Homology of a Coproduct
15.The Universal Coefficient Theorem and the (Co) Homology of a Product
16.Groups and Subgroups
Ⅶ.Cohomology of Lie Algebras
1.Lie Algebras and their Universal Enveloping Algebra
2.Definition of Cohomology; H0, H1
3.H2 and Extensions
4.A Resolution of the Ground Field K
5.Semi-simple Lie Algebras
6.The two Whitehead Lemmas
7.Appendix: Hilbert’s Chain-of-Syzygies Theorem
Ⅷ.Exact Couples and Spectral Sequences
1.Exact Couples and Spectral Sequences
2.Filtered Differential Objects
3.Finite Convergence Conditions for Filtered Chain Complexes
4.The Ladder of an Exact Couple
5.Limits
6.Rees Systems and Filtered Complexes
7.The Limit of a Rees System
8.Completions of Filtrations
9.The Grothendieck Spectral Sequence
Ⅸ.Satellites and Homology
I.Projective Classes of Epimorphisms
2.ε-Derived Functors
3.ε-Satellites
4.The Adjoint Theorem and Examples
5.Kan Extensions and Homology
6.Applications: Homology of Small Categories, Spectral Sequences
Ⅹ.Some Applications and Recent Developments
I.Homological Algebra and Algebraic Topology
2.Nilpotent Groups
3.Finiteness Conditions on Groups
4.Modular Representation Theory
5.Stable and Derived Categories
Bibliography
Index
Introduction
Ⅰ.Modules
1.Modules
2.The Group of Homomorphisms
3.Sums and Products
4.Free and Projective Modules
5.Projective Modules over a Principal Ideal Domain
6.Dualization, Injective Modules
7.Injective Modules over a Principal Ideal Domain
8.Cofree Modules
9.Essential Extensions
Ⅱ.Categories and Functors
1.Categories
2.Functors
3.Duality
4.Natural Transformations
5.Products and Coproducts; Universal Constructions
6.Universal Constructions (Continued); Pull-backs and Push-outs
7.Adjoint Functors
8.Adjoint Functors and Universal Constructions
9.Abelian Categories
10.Projective, Injective, and Free Objects
Ⅲ.Extensions of Modules
1.Extensions
2.The Functor Ext
3.Ext Using Injectives
4.Computation of some Ext-Groups
5.Two Exact Sequences
6.A Theorem of Stein-Serre for Abelian Groups
7.The Tensor Product
8.The Functor Tor
Ⅳ.Derived Funetors
1.Complexes
2.The Long Exact (Co) Homology Sequence
3.Homotopy
4.Resolutions
5.Derived Functors
6.The Two Long Exact Sequences of Derived Functor
7.The Functors ExtnΛ Using Projectives
8.The Functors ExtnΛ Using Injectives
9.Extn and n-Extensions
10.Another Characterization bfDerived Functors
11.The Functor TotΛn
12.Change of Rings
Ⅴ.The Kunneth Formula
1.Double Complexes
2.The Kiinneth Theorem
3.The Dual Kunneth Theorem
4.Applications of the Kunneth Formulas
Ⅵ.Cohomology of Groups
1.The Group Ring
2.Definition of (Co) Homology
3.H0, H0
4.H1, H1 with Trivial Coefficient Modules
5.The Augmentation Ideal, Derivations, and the Semi-Direct Product
6.A Short Exact Sequence
7.The (Co) Homology of Finite Cyclic Groups
8.The 5-Term Exact Sequences
9.H2, Hopf’s Formula, and the Lower Central Series
10.H2 and Extensions
11.Relative Projeetives and Relative Injectives
12.Reduction Theorems
13.Resolutions
14.The (Co) Homology of a Coproduct
15.The Universal Coefficient Theorem and the (Co) Homology of a Product
16.Groups and Subgroups
Ⅶ.Cohomology of Lie Algebras
1.Lie Algebras and their Universal Enveloping Algebra
2.Definition of Cohomology; H0, H1
3.H2 and Extensions
4.A Resolution of the Ground Field K
5.Semi-simple Lie Algebras
6.The two Whitehead Lemmas
7.Appendix: Hilbert’s Chain-of-Syzygies Theorem
Ⅷ.Exact Couples and Spectral Sequences
1.Exact Couples and Spectral Sequences
2.Filtered Differential Objects
3.Finite Convergence Conditions for Filtered Chain Complexes
4.The Ladder of an Exact Couple
5.Limits
6.Rees Systems and Filtered Complexes
7.The Limit of a Rees System
8.Completions of Filtrations
9.The Grothendieck Spectral Sequence
Ⅸ.Satellites and Homology
I.Projective Classes of Epimorphisms
2.ε-Derived Functors
3.ε-Satellites
4.The Adjoint Theorem and Examples
5.Kan Extensions and Homology
6.Applications: Homology of Small Categories, Spectral Sequences
Ⅹ.Some Applications and Recent Developments
I.Homological Algebra and Algebraic Topology
2.Nilpotent Groups
3.Finiteness Conditions on Groups
4.Modular Representation Theory
5.Stable and Derived Categories
Bibliography
Index
