图书介绍
A course in homological algebraPDF|Epub|txt|kindle电子书版本下载
- PJ Hilton，U Stammbach 著
- 出版社： 世界图书出版公司
- ISBN：7506260077
- 出版时间：2003
- 标注页数：364页
- 文件大小：54MB
- 文件页数：376页
- 主题词：
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图书目录
Introduction1
Ⅰ．Modules10
1．Modules11
2．The Group of Homomorphisms16
3．Sums and Products18
4．Free and Projective Modules22
5．Projective Modules over a Principal Ideal Domain26
6．Dualization,Injective Modules28
7．Injective Modules over a Principal Ideal Domain31
8．Cofree Modules34
9．Essential Extensions36
Ⅱ．Categories and Functors40
1．Categories40
2．Functors44
3．Duality48
4．Natural Transformations50
5．Products and Coproducts：Universal Constructions54
6．Universal Constructions（Continued）；Pull-backs and Push-outs59
7．Adjoint Functors63
8．Adjoint Functors and Universal Constructions69
9．Abelian Categories74
10．Projective,Injective,and Free Objects81
Ⅲ．Extensions of Modules84
1．Extensions84
2．The Functor Ext89
3．Ext Using Injectives94
4．Computation of some Ext-Groups97
5．Two Exact Sequences99
6．A Theorem of Stein-Serre for Abelian Groups106
7．The Tensor Product109
8．The Functor Tor112
Ⅳ．Derived Functors116
1．Complexes117
2．The Long Exact（Co）Homology Sequence121
3．Homotopy124
4．Resolutions126
5．Derived Functors130
6．The Two Long Exact Sequences of Derived Functors136
7．The Functors Extn ∧ Using Projectives139
8．The Functors？Using Injectives143
9．Extn and n-Extensions148
10．Another Characterization of Derived Functors156
11．The Functor Tor∧ n160
12．Change of Rings162
Ⅴ．The Künneth Formula166
1．Double Complexes167
2．The Künneth Theorem172
3．The Dual Künneth Theorem177
4．Applications of the Künneth Formulas180
Ⅵ．Cohomology of Groups184
1．The Group Ring186
2．Definition of（Co）Homology188
3．H0,H0191
4．H1,H1 with Trivial Coefficient Modules192
5．The Augmentation Ideal,Derivations,and the Semi-Direct Product194
6．A Short Exact Sequence197
7．The（Co）Homology of Finite Cyclic Groups200
8．The 5-Term Exact Sequences202
9．H2,Hopf's Formula,and the Lower Central Series204
10．H2 and Extensions206
11．Relative Projectives and Relative Injectives210
12．Reduction Theorems213
13．Resolutions214
14．The（Co）Homology of a Coproduct219
15．The Universal Coefficient Theorem and the（Co）Homology of a Product221
16．Groups and Subgroups223
Ⅶ．Cohomology of Lie Algebras229
1．Lie Algebras and their Universal Enveloping Algebra229
2．Definition of Cohomology；H0,H1234
3．H2 and Extensions237
4．A Resolution of the Ground Field K239
5．Semi-simple Lie Algebras244
6．The two Whitehead Lemmas247
7．Appendix：Hilbert's Chain-of-Syzygies Theorem251
Ⅷ．Exact Couples and Spectral Sequences255
1．Exact Couples and Spectral Sequences256
2．Filtered Differential Objects261
3．Finite Convergence Conditions for Filtered Chain Complexes265
4．The Ladder of an Exact Couple269
5．Limits276
6．Rees Systems and Filtered Complexes281
7．The Limit of a Rees System288
8．Completions of Filtrations291
9．The Grothendieck Spectral Sequence297
Ⅸ．Satellites and Homology306
1．Projective Classes of Epimorphisms307
2．E-Derived Functors309
3．E-Satellites312
4．The Adjoint Theorem and Examples318
5．Kan Extensions and Homology320
6．Applications：Homology of Small Categories,Spectral Sequences327
Ⅹ．Some Applications and Recent Developments331
1．Homological Algebra and Algebraic Topology331
2．Nilpotent Groups335
3．Finiteness Conditions on Groups339
4．Modular Representation Theory344
5．Stable and Derived Categories349
Bibliography357
Index359