《同調代數導論（第2版）》是2015年7月1日世界圖書出版公司出版的著作，作者是Joseph、J.Rotman 。
基本介紹
- 中文名：《同調代數導論（第2版）》
- 作者：Joseph、J.Rotman
- 出版社：世界圖書出版公司
- 出版時間：2015年07月01日
- ISBN：9787510098529
內容簡介,目錄,
內容簡介
《同調代數導論（第2版 英文版）》既有大量例題，又有許多代數套用。《同調代數導論（第2版 英文版）》內容清晰、易於遵循。作者用代數拓撲學中的與之同源的名詞術語解釋了同調代數的解的過程。在該全新的版本中，全文都做了更新和徹底地修訂，並且新增了層論和交換範疇的內容。
目錄
Preface to the Second Edition
How to Read This Book
Chapter 1 Introduction
1．1 SimpliciaIHomology
1．2 Categories and Functors
1．3 Singular Homology
Chapter 2 Hom and Tensor
2．1 Modules
2．2 Tensor Products
2．2．1 Adjointlsomorphisms
Chapter 3 Special Modules
3．1 Projective Modules
3．2 InjectiveModules
3．3 Flat Modules
3．3．1 Purity
Chapter 4 Specific Rings
4．1 Semisimple Rings
4．2 von Neumann Regular Rings
4．3 Hereditary and Dedekind Rings
4．4 Semihereditary and Prufer Rings
4．5 Quasi-Frobenius Rings
4．6 Semiperfect Rings
4．7 Localization
4．8 Polynomial Rings
Chapter 5 Setting the Stage
5．1 Categorical Constructions
5．2 Limits
5．3 Adjoint Functor Theorem for Modules
5．4 Sheaves
5．4．1 Manifolds
5．4．2 Sheaf Constructions
5．5 Abelian Categories
5．5．1 Complexes
Chapter 6 Homology
6．1 Homology Functors
6．2 Derived Functors
6．2．1 Left Derived Functors
6．2．2 Axioms
6．2．3 Covariant Right Derived Functors
6．2．4 Contravariant Right Derived Functors
6．3 Sheaf Cohomology
6．3．1 Cech Cohomology
6．3．2 Riemann-Roch Theorem
Chapter 7 Tor and Ext
7．1 Tor
7．1．1 Domains
7．1．2 Localization
7．2 Ext
7．2．1 Baer Sum
7．3 Cotorsion Groups
7．4 Universal Coefficients
Chapter 8 Homology and Rings
8．1 Dimensions ofRings
8．2 Hilbert's Syzygy Theorem
8．3 Stably Free Modules
8．4 Commutative Noetherian Local Rings
Chapter 9 Homology and Groups
9．1 Group Extensions
9．1．1 Semidirect Products
9．1．2 General Extensions and Cohomology
9．1．3 Stabilizing Automorphisms
9．2 Group Cohomology
9．3 Bar Resolutions
9．4 Group Homology
9．4．1 Schur Multiplier
9．5 Change of Groups
9．5．1 Restriction and Inflation
9．6 Transfer
9．7 Tate Groups
9．8 Outer Automorphisms of p-Groups
9．9 Cohomological Dimension
9．10 Division Rings and Brauer Groups
Chapter 10 Spectral Sequences
10．1 Bicomplexes
10．2 Filtrations and Exact Couples
10．3 Convergence
10．4 Homology of the Total Complex
10．5 Cartan-Eilenberg Resolutions
10．6 Grothendieck Spectral Sequences
10．7 Groups
10．8 Rings
10．9 Sheaves
10．10 Kunneth Theorems
References
Special Notation
Index
