I. ALGEBRAIC PRELIMINARIES
- Homomorphisms and extensions.
- Direct sums and products.
- Linear topologies.
II. SET THEORY
- Ordinary set theory.
- Filters and large cardinals.
- Clubs and stationary sets.
- Games and trees.
- ▵-systems and partitions.
III. SLENDER MODULES
1.Introduction to slenderness.
2.Examples of slender modules and rings.
3.The Łoś-Eda theorem.
IV. ALMOST FREE MODULES
- Introduction to ℵ1free abelian groups.
- &kgr;-free modules.
- ℵ1-free abelian groups.
- Compactness results.
V. PURE INJECTIVE MODULES
- Structure theory.
- Cotorsion groups.
VI. MORE SET THEORY
- Prediction Principles.
- Models of set theory.
- L, the constructible universe.
- MA and PFA.
- PCF theory and I[&lgr;].
VII. ALMOST FREE MODULES REVISISTED (IV, VI)
- ℵ1-free abelian groups revisited.
- &kgr;-free modules revisited.
- &kgr;-free abelian groups.
- Transversals, &lgr;-systems and NPT.
3A. Reshuffling &lgr;-systems.
- Hereditarily separable groups.
- NPT and the construction of almost free groups.
VIII. ℵ1-SEPARABLE GROUPS (VI, VII.0,1)
- Constructions and definitions.
- ℵ1-separable groups under Martin's axiom.
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.
University Mathematical Libraries, Mathematics Departments and Research Institutes.
- No. of pages:
- © North Holland 2002
- 29th April 2002
- North Holland
- eBook ISBN:
- Hardcover ISBN:
Department of Mathematics, University of California, Irvine, CA 92697-3875 USA