
- 620 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
About this book
This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and udated to include major developments in the decade since the first edition. Among these are applications to cotorsion theories and covers, including a proof of the Flat Cover Conjecture, as well as the use of Shelah's pcf theory to constuct almost free groups. As with the first edition, the book is largely self-contained, and designed to be accessible to both graduate students and researchers in both algebra and logic. They will find there an introduction to powerful techniques which they may find useful in their own work.
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Information
Table of contents
- Cover image
- Title page
- Table of Contents
- Copyright page
- Dedication
- Preface to the revised edition
- Preface
- Chapter I: Algebraic Preliminaries
- Chapter II: Set Theory
- Chapter III: Slender Modules
- Chapter IV: Almost Free Modules
- Chapter V: Pure-Injective Modules
- Chapter VI: More Set Theory
- Chapter VII: Almost Free Modules Revisited
- Chapter VIII: ℵ1-Separable Groups
- Chapter IX: Quotients of Products of Z
- Chapter X: Iterated Sums and Products
- Chapter XI: Topological Methods
- Chapter XII: An Analysis of EXT
- Chapter XIII: Uniformization
- Chapter XIV: The Black Box and Endomorphism Rings
- Chapter XV: Some Constructions in ZFC
- Chapter XVI: Cotorsion Theories, Covers and Splitters
- Chapter XVII: Dual Groups
- Appendix: Open and Solved Problems
- Bibliography
- Index