five years ago, i taught a one-quarter course in homological algebra. i discovered that there was no book which was really suitable as a text for such a short course, so i decided to write one. the point was to cover both ext and tot early, and still have enough material for a larger course (one semester or two quarters) going off in any of several possible directions. this book is 'also intended to be readable enough for independent study.
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 Abelin Categories 7.7 Long Exact Sequences 7.8 An Alternative for Unbalanced Categories 8 Colimits and Tor 9 Odds and Ends A GCDs，LCMs，PIDs，and UFDs B The Ring of Entire Functions C The Mitchell-Ereyd Theorem and Cheating in Abelian Cat-egories D Noether Correspondences in Abelian Categories Solution Outlines References Symbol Index Index
