Almost Free Modules: Set-theoretic Methods (Google eBook)

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Elsevier, Apr 29, 2002 - Mathematics - 620 pages
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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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Contents

Chapter I ALGEBRAIC PRELIMINARIES
1
Chapter II SET THEORY
17
Chapter III SLENDER MODULES
55
Chapter IV ALMOST FREE MODULES
85
Chapter V PURE INJECTIVE MODULES
123
Chapter VI MORE SET THEORY
143
Chapter VII ALMOST FREE MODULES REVISISTED IV VI
191
Chapter VIII N1SEPARABLE GROUPS VI VII0 1
264
Chapter XII AN ANALYSIS OF EXT VII VIII1
363
Chapter XIII UNIFORMIZATION XII
401
Chapter XIV THE BLACK BOX AND ENDOMORPHISM RINGS V VI
441
Chapter XV SOME CONSTRUCTIONS IN ZFC VII VIII XIV
476
Chapter XVI COTORSION THEORIES COVERS AND SPLITTERS IX XII1 XIV
498
Chapter XVII DUAL GROUPS IX XI XIV
527
OPEN AND SOLVED PROBLEMS
559
Bibliography
563

Chapter IX QUOTIENTS OF PRODUCTS OF Z III IV V
292
Chapter X ITERATED SUMS AND PRODUCTS III
316
Chapter XI TOPOLOGICAL METHODS X IV
328

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Page ii - North-Holland Mathematical Library Board of Advisory Editors: M. Artin, H. Bass, J. Eells, W. Feit, PJ Freyd, FW Gehring, H. Halberstam, LV Hormander, M.
Page 23 - X -D. It turns out that a filter over / is an ultrafilter if and only if it is a maximal filter over / (ie, there is no larger filter containing it). One can show, using Zorn's lemma, that if...
Page 565 - Locally free modules and a problem of Whitehead, Illinois J. Math. 6, 682-699.
Page 589 - Non-perfect rings and a theorem of Eklof and Shelah, Comment. Math. Univ. Carolinae 32, 27-32.

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