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Almost free modules : set-theoretic methods / Paul C. Eklof, Alan H. Mekler
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: North-Holland mathematical library ; 46Publisher: Amsterdam ; New York ; New York, N.Y., U.S.A : North-Holland, 1990Description: Online Ressource (xvi, 481 p.)ISBN:- 9780080960241
- 0080960243
- 0444885021
- 9780444885029
- QA247
Contents:
Summary: Cover13; -- Almost Free Modules: Set-theoretic Methods -- Copyright Page -- TABLE OF CONTENTS -- CHAPTER I ALGEBRAIC PRELIMINARIES -- 1. Homomorphisms and extensions -- 2. Direct sums and products -- 3. Linear topologies -- CHAPTER II SET THEORY -- 1. Ordinary set theory -- 2. Filters and large cardinals -- 3. Ultraproducts -- 4. Cubs and stationary sets -- 5. Games and trees -- Exercises -- Notes -- CHAPTER III SLENDER MODULES -- 1. Introduction to slenderness -- 2. Examples of slender modules and rings -- 3. The Lo347;-Eda theorem -- Exercises -- Notes -- CHAPTER IV ALMOST FREE MODULES -- 1. k-free modules -- 2. N1-free abelian groups -- 3. Compactness results -- Exercises -- Notes -- CHAPTER V PURE-INJECTIVE MODULES -- 1. Structure theory -- 2. Cotorsion groups -- Exercises -- Notes -- CHAPTER VI MORE SET THEORY -- 1. Prediction principles -- 2. Models of set theory -- 3. L, the constructible universe -- 4. MA and PFA -- Exercises -- Notes -- CHAPTER VII ALMOST FREE MODULES REVISITED (IV, VI) -- 1. k-free modules revisited -- 2. k-free abelian groups -- 3. Transversals and 955;-systems -- 3A. Reshuffling 955;-systems -- 4. Hereditarily separable groups -- Exercises -- Notes -- CHAPTER VIII COUNTABLY-SEPARABLE GROUPS (VI, VII.l) -- 1. Constructions and definitions -- 2. N1-separable groups under Martins axiom -- 3. N1-separable groups under PFA -- Exercises -- Notes -- CHAPTER IX QUOTIENTS OF PRODUCTS OF THE INTEGERS (III, IV, V) -- 1. Perps and products -- 2. Countable products of the integers -- 3. Uncountable products of the integers -- 4. Radicals and large cardinals -- Exercises -- Notes -- CHAPTER X ITERATED SUMS AND PRODUCTS (III) -- 1. The Reid class -- 2. Types in the Reid class -- Exercises -- Notes -- CHAPTER XI TOPOLOGICAL METHODS (X, IV) -- 1. Inverse and direct limits -- 2. Completions -- 3. Density and dual bases -- 4. Groups of continuous functions -- Exercises -- Notes -- CHAPTER XII THE STRUCTURE OF EXT (VII, VIII.l) -- 1. The vanishing of Ext -- 2. The rank of Ext -- 3. Uniformization and W-groups -- Exercises -- Notes -- CHAPTER XIII THE BLACK BOX AND ENDOMORPHISM RINGS (V, VI) -- 1. Black Box -- 2. Proof of the Black Box -- 3. Endomorphism rings of cotorsion-free groups -- 4. Endomorphism rings of separable groups -- Exercises -- Notes -- CHAPTER XIV DUAL GROUPS (IX, XI, XIII) -- 1. Invariants of dual groups -- 2. Tree groups -- 3. Criteria for being a dual group -- 4. Some non-reflexive dual groups -- 5. More dual groups -- Notes -- OPEN PROBLEMS -- BIBLIOGRAPHY -- INDEXSummary: This is an extended treatment of the set-theoretic techniques which have transformed the study of abelian group and module theory over the last 15 years. Part of the book is new work which does not appear elsewhere in any form. In addition, a large body of material which has appeared previously (in scattered and sometimes inaccessible journal articles) has been extensively reworked and in many cases given new and improved proofs. The set theory required is carefully developed with algebraists in mind, and the independence results are derived from explicitly stated axioms. The book contains exePPN: PPN: 1657822443Package identifier: Produktsigel: BSZ-33-ECE | ZDB-33-MTC | BSZ-33-EBS-C1UB | BSZ-33-EBS-HSAA | GBV-33-EBS-MRI | GBV-33-EBS-ZHB | GBV-33-Freedom-BL | ZDB-33-CEN | ZDB-1-ELC | ZDB-33-EBS | ZDB-33-ESD
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