既有大量例題，又有許多代數應用，該書真是一本必讀書：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。 目次：導言； Hom 和 Tensor函子；特殊模；特定環；創建平臺；同源性；Tor 和 Ext函子；同調性和環；同調性和群；譜序列；參考文獻；特殊符號；索引。
目錄
Preface to the Second Edition
How to Read This Book
Chapterl 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
Chapter6 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
作者介紹
Joseph J. Rotman (J.J.羅特曼)是國際知名學者，在數學界享有盛譽。本書凝聚了作者多年科研和教學成果，適用于科研工作者、高校教師和研究生。
