同調代數導論（第2版 英文版） [An Introduction To Homological Algebra] 下載 mobi epub pdf 電子書 2024

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內容簡介

　　《同調代數導論（第2版 英文版）》既有大量例題，又有許多代數應用。《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瞭同調代數的解的過程。在該全新的版本中，全文都做瞭更新和徹底地修訂，並且新增瞭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
同調代數導論（第2版 英文版） [An Introduction To Homological Algebra] 下載 mobi epub pdf txt 電子書 格式

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