Basic homological algebra
Author(s)
Bibliographic Information
Basic homological algebra
（Graduate texts in mathematics, 196）
Springer, c2000
- : softcover
Available at / 99 libraries
-
No Libraries matched.
- Remove all filters.
Note
"c2000 Springer Science+Business Media New York. Originally published by Springer-Verlag New York in 2000. Softcover reprint of the hardcover 1st edition 2002 [sic]"--T.p. of softcover
Includes bibliographical references (p. [383]-387) and indexes
Description and Table of Contents
Description
From the reviews: "The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [...] I especially appreciated the lively style of the book; [...] one is quickly able to find necessary details." EMS Newsletter
Table of Contents
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 Homologieal 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 Kunneth Theorems.- 9.4 Do Connecting Homomorphisms Commute?.- 9.5 The Ext Product.- 9.6 The Jacobson 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 Categories.- D Noether Correspondences in Abelian Categories.- Solution Outlines.- References.- Symbol Index.
by "Nielsen BookData"