Almost Free Modules: Set-Theoretic Methods

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Elsevier, Apr 23, 1990 - Mathematics - 480 pages
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 exercises and a guide to the literature and is suitable for use in graduate courses or seminars, as well as being of interest to researchers in algebra and logic.
 

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Contents

CHAPTER I ALGEBRAIC PRELIMINARIES
1
CHAPTER II SET THEORY
16
CHAPTER III SLENDER MODULES
51
CHAPTER IV ALMOST FREE MODULES
82
CHAPTER V PUREINJECTIVE MODULES
118
CHAPTER VI MORE SET THEORY
138
CHAPTER VII ALMOST FREE MODULES REVISITED IV VI
180
CHAPTER VIII COUNTABLYSEPARABLE GROUPS VI VIIl
247
CHAPTER X ITERATED SUMS AND PRODUCTS III
300
CHAPTER XI TOPOLOGICAL METHODS X IV
313
CHAPTER XII THE STRUCTURE OF EXT VIIVIIIl
344
CHAPTER XIII THE BLACK BOX AND ENDOMORPHISM RINGS V VI
389
CHAPTER XIV DUAL GROUPS IX XI XIII
420
OPEN PROBLEMS
453
BIBLIOGRAPHY
456
INDEX
477

CHAPTER IX QUOTIENTS OF PRODUCTS OF THE INTEGERS III IV V
276

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