《基本同调代数》(Basic Homological Algebra)扫描英文版[DJVU]

类别:: 图书 - 教育科技
状态:: 普通资源
发布:: 2010-04-20 19:56:00
更新:: 2012-09-12 12:08:00

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电驴资源简介

资源介绍

语言: 英文

地区: 大陆

图书fenlei: 科技

中文名: 基本同调代数

发行时间: 2003年

原名: Basic Homological Algebra

资源格式: DJVU

版本: 扫描英文版

简介:

djvu　阅读器：　http://windjview.sourceforge.net/
内容简介：
本书主要介绍了同调代数学中的基本理论，内容包括：范畴，模，函子Ext和Tor，维数理论，环的变化，抽象同调代数等。本书编排合理，条理清晰，内容由浅入深，除介绍同调代数学中的基本理论外，还增加了一些在相关书中很少涉及的有一定难度与深度的内容，例如Lazard定理等。
目次：范畴；模；函子Ext和Tor；维数理论；环的变换；导函数；抽象同调代数；方向极限与Tor函子；其它。
读者对象: 高等院校理科类研究生及教师。
内容截图：

目录: Preface
1 Categories
2 Modules
2.1 Generalities
2.2 Tensor Products
2.3 Exactness of Functors
2.4 Projectives, Injectives, and Flats
3 Ext and Tor
3.1 Complexes and Projective Resolutions
3.2 Long Exact Sequences
3.3 Flat Resolutions and Injective Resolutions
3.4 Consequences
4 Dimension Theory
4.1 Dimension Shifting
4.2 When Flats are Projective
4.3 Dimension Zero
4.4 An Example
5 Change of Rings
5.1 Computational Considerations
5.2 Matrix Rings
5.3 Polynomials
5.4 Quotients and Localization
6 Derived Functors
6.1 Additive Functors
6.2 Derived Functors
6.3 Long Exact Sequences——Ⅰ. Existence
6.4 Long Exact Sequences——Ⅱ. Naturality
6.5 Long Exact Sequences——Ⅲ. Weirdness
6.6 Universality of Ext
7 Abstract Homological Algebra
7.1 Living Without Elements
7.2 Additive Categories
7.3 Kernels and Cokernels
7.4 Cheating with Projectives
7.5 (Interlude) Arrow Categories
7.6 Homology in Abelian Categories
7.7 Long Exact'Sequences
7.8 An Alternative for Unbalanced Categories
8 Colimits and Tor
8.1 Limits and Colimits
8.2 Adjoint Functors
8.3 Directed Colimits and Tor
8.4 Lazard's Theorem
8.5 Weak Dimension Revisited
9 Odds and Ends
9.1 Injective Envelopes
9.2 UniVersal Coefficients
9.3 The Kiinneth Theorems
9.4 Do Connecting Homomorphisms Commute?
9.5 The Ext Product
9.6 The 3acobson Radical, Nakayama's Lemma, and Quasilocal Rings
9.7 Local Rings and Localization Revisited (Expository)
A GCDs, LCMs, PIDs, and UFDs
B The Ring of Entire Functions
C The Mitchell-Freyd Theorem and Cheating in Abelian Cat egories
D Noether Correspondences in Abelian Categories
Solution Outlines
References
Symbol Index
Index