內容簡介
《基本周調代數(英文版)》內容簡介：Fiveyearsago,Itaughtaone-quartercourseinhomologicalalgebra.Idiscoveredthattherewasnobookwhichwasreallysuitableasatextforsuchashortcourse,soIdecidedtowriteone.ThepointwastocoverbothExtandTotearly,andstillhaveenoughmaterialforalargercourse(onesemesterortwoquarters)goingoffinanyofseveralpossibledirections.Thisbookis'alsointendedtobereadableenoughforindependentstudy. {zzjj}
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
叢書信息
Graduate Texts in Mathematics (共158冊), 這套叢書還有 《加性數論》,《復變導論》,《機率論(第1卷)》,《偏微分方程.第2版》,《黎曼曲面》 等。
