導讀： 資源介紹 語言: 英文 地區: 大陸 圖書fenlei: 科技 中文名: 基本同調代數 發行時間: 2003年 原名: Basic Homological Algebra 資源格式: DJVU 版本: 掃描英文版 簡介: djvu閱讀器：http://windjview.sourcef 資源介紹 語言: 英文 地區: 大陸 圖書fenlei: 科技 中文名: 基本同調代數 發行時間: 2003年 原名: Basic Homological Algebra 資源格式: DJVU 版本: 掃描英文版 簡介:
djvu　閱讀器：　http://windjview.sourceforge.net/
內容簡介：
本書主要介紹了同調代數學中的基本理論，內容包括：范疇，模，函子Ext和Tor，維數理論，環的變化，抽象同調代數等。本書編排合理，條理清晰，內容由淺入深，除介紹同調代數學中的基本理論外，還增加了一些在相關書中很少涉及的有一定難度與深度的內容，例如Lazard定理等。
目次：范疇；模；函子Ext和Tor；維數理論；環的變換；導函數；抽象同調代數；方向極限與Tor函子；其它。
讀者對象: 高等院校理科類研究生及教師。
內容截圖：
目錄: 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