An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and often, this involves yet another language: spectral sequences. Homological algebra is an accessible subject to those who wish to learn it, and this book is the author’s attempt to make it lovable.
This book comprises 11 chapters, with an introductory chapter that focuses on line integrals and independence of path, categories and functors, tensor products, and singular homology. Succeeding chapters discuss Hom and Ⓧ; projectives, injectives, and flats; specific rings; extensions of groups; homology; Ext; Tor; son of specific rings; the return of cohomology of groups; and spectral sequences, such as bicomplexes, Kunneth Theorems, and Grothendieck Spectral Sequences.
This book will be of interest to practitioners in the field of pure and applied mathematics.
1. Chapter 1: Introduction - p. v 2. Chapter 2: Hom and - p. 22 3. Chapter 3: Projectives, Injectives, and Flats - p. 56 4. Chapter 4: Specific Rings - p. 107 5. Chapter 5: Extensions of Groups - p. 149 6. Chapter 6: Homology - p. 165 7. Chapter 7: Ext - p. 193 8. Chapter 8: Tor - p. 219 9. Chapter 9: Son of Specific Rings - p. 231 10. Chapter 10: The Return of Cohomology of Groups - p. 264 11. Chapter 11: Spectral Sequences - p. 298 12. References - p. 366 13. Index - p. 369 14. Pure and Applied Mathematics - p. 369
An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and often, this involves yet another language: spectral sequences. Homological algebra is an accessible subject to those who wish to learn it, and this book is the author’s attempt to make it lovable.
This book comprises 11 chapters, with an introductory chapter that focuses on line integrals and independence of path, categories and functors, tensor products, and singular homology. Succeeding chapters discuss Hom and Ⓧ; projectives, injectives, and flats; specific rings; extensions of groups; homology; Ext; Tor; son of specific rings; the return of cohomology of groups; and spectral sequences, such as bicomplexes, Kunneth Theorems, and Grothendieck Spectral Sequences.
This book will be of interest to practitioners in the field of pure and applied mathematics.
1. Chapter 1: Introduction - p. v 2. Chapter 2: Hom and - p. 22 3. Chapter 3: Projectives, Injectives, and Flats - p. 56 4. Chapter 4: Specific Rings - p. 107 5. Chapter 5: Extensions of Groups - p. 149 6. Chapter 6: Homology - p. 165 7. Chapter 7: Ext - p. 193 8. Chapter 8: Tor - p. 219 9. Chapter 9: Son of Specific Rings - p. 231 10. Chapter 10: The Return of Cohomology of Groups - p. 264 11. Chapter 11: Spectral Sequences - p. 298 12. References - p. 366 13. Index - p. 369 14. Pure and Applied Mathematics - p. 369
