LIMITED OFFER

## Save 50% on book bundles

Immediately download your ebook while waiting for your print delivery. No promo code is needed.

Skip to main content# Almost Free Modules

## Set-theoretic Methods

## Purchase options

## Save 50% on book bundles

## Institutional subscription on ScienceDirect

Request a sales quote### P.C. Eklof

Save up to 30% on Elsevier print and eBooks with free shipping. No promo code needed.

Save up to 30% on print and eBooks.

1st Edition, Volume 65 - April 29, 2002

Authors: P.C. Eklof, A.H. Mekler

Language: EnglishHardback ISBN:

9 7 8 - 0 - 4 4 4 - 5 0 4 9 2 - 0

eBook ISBN:

9 7 8 - 0 - 0 8 - 0 5 2 7 0 5 - 5

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… Read more

LIMITED OFFER

Immediately download your ebook while waiting for your print delivery. No promo code is needed.

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.

I. ALGEBRAIC PRELIMINARIES1. Homomorphisms and extensions.2. Direct sums and products.3. Linear topologies. II. SET THEORY1. Ordinary set theory.2. Filters and large cardinals.3. Ultraproducts.4. Clubs and stationary sets.5. Games and trees.6. ▵-systems and partitions.III. SLENDER MODULES1.Introduction to slenderness.2.Examples of slender modules and rings.3.The Łoś-Eda theorem.IV. ALMOST FREE MODULES0. Introduction to ℵ1free abelian groups.1. &kgr;-free modules.2. ℵ1-free abelian groups.3. Compactness results.V. PURE INJECTIVE MODULES1. Structure theory.2. Cotorsion groups.VI. MORE SET THEORY1. Prediction Principles.2. Models of set theory.3. L, the constructible universe.4. MA and PFA.5. PCF theory and *I*[&lgr;]. VII. ALMOST FREE MODULES REVISISTED (IV, VI)0. ℵ1-free abelian groups revisited.1. &kgr;-free modules revisited.2. &kgr;-free abelian groups.3. Transversals, &lgr;-systems and NPT.3A. Reshuffling &lgr;-systems.4. Hereditarily separable groups.5. NPT and the construction of almost free groups.VIII. ℵ1-SEPARABLE GROUPS (VI, VII.0,1)1. Constructions and definitions.2. ℵ1-separable groups under Martin's axiom.3. ℵ1-separable groups under PFA.IX. QUOTIENTS OF PRODUCTS OF Z(III, IV, V)1. Perps and products.2. Countable products of the integers.3. Uncountable products of the integers.4. Radicals and large cardinals.X. ITERATED SUMS AND PRODUCTS (III)1. The Reid class.2. Types in the Reid class.XI. TOPOLOGICAL METHODS (X, IV)1. Inverse and direct limits.2. Completions.3. Density and dual bases.4. Groups of continuous functions.5. Sheaves of abelian groups.XII. AN ANALYSIS OF EXT (VII, VIII.1)1. Ext and Diamond.2. Ext, MA and Proper forcing.3. Baer modules.4. The structure of Ext.5. The structure of Ext when Hom=0. XIII. UNIFORMIZATION (XII)0. Whitehead groups and uniformization.1. The basic construction and its applications.2. The necessity of uniformization.3. The diversity of Whitehead groups.4. Monochromatic uniformization and hereditarily separable groups.XIV. THE BLACK BOX AND ENDOMORPHISM RINGS(V, VI)1. Introducing the Black Box.2. Proof of the Black Box.3. Endomorphism rings of cotorsion-free groups.4. Endomorphism rings of separable groups.5. Weak realizability of endomorphism rings and the Kaplansky Test problems.XV. SOME CONSTRUCTIONS IN ZFC (VII, VIII, XIV)1. A rigid ℵ1-free group of cardinality ℵ1.2. ℵn-separable groups with the Corner pathology.3. Absolutely indecomposable modules.4. The existence of &lgr;-separable groups.XVI. COTORSION THEORIES, COVERS AND SPLITTERS(IX, XII.1, XIV)1. Orthogonal classes and splitters.2. Cotorsion theories.3. Almost free splitters.4. The Black Box and Ext.XVII. DUAL GROUPS (IX, XI, XIV)1. Invariants of dual groups.2. Tree groups.3. Criteria for being a dual group.4. Some non-reflexive groups.5. Dual groups in L.

- No. of pages: 620
- Language: English
- Edition: 1
- Volume: 65
- Published: April 29, 2002
- Imprint: North Holland
- Hardback ISBN: 9780444504920
- eBook ISBN: 9780080527055

PE

Affiliations and expertise

Department of Mathematics, University of California, Irvine, CA 92697-3875 USARead *Almost Free Modules* on ScienceDirect