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同調代數教程 第2版 版權信息
- ISBN:9787506260077
- 條形碼:9787506260077 ; 978-7-5062-6007-7
- 裝幀:一般膠版紙
- 冊數:暫無
- 重量:暫無
- 所屬分類:>>
同調代數教程 第2版 內容簡介
本書是一本比較標準的同調代數教材,從60年代末開始在瑞士聯邦理工學院及美國幾所大學使用,第1版曾重印3次, 本版在第1版的基礎上增加了新內容——同調代數的應用和新展。本書內容比較詳細全面,基礎理論十分扎實;論述也比較深入淺出,通俗易懂,有很好的例題和習題。本書第1版曾編為W1/4。目次:模;范疇與函子;模的擴張;導出函子;Kunneth公式;群的上同調;李代數的上同調;正合偶和譜序列;伴隨性和同調論;應用和*新進展。
同調代數教程 第2版 目錄
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
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同調代數教程 第2版 作者簡介
P.J.Hilton,紐約州立大學賓漢姆頓分校(State University of New York Binghamton)數學系教授,A Course in Homological Algebra和Symposium on Algebraic Topology很受讀者認可。
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