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

1 | |

17 | |

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 |

563 | |

### Common terms and phrases

81-free group A-free abelian group assume belongs Black Box cardinality R1 choose clopen club cofinality construction contained contradiction Corollary cotorsion countable sets define definition denote direct sum direct summand disjoint dual group element Exercise exists Ext(A finite subset free group free module function group of cardinality hence Hint holds homomorphism hypothesis implies increasing sequence induction isomorphic k-complete k-filtration ladder system Lemma Let F limit ordinal Moreover n e Sf n e w non-free non-zero p-adic predual prime projective PROOF Proposition prove pure subgroup pure-injective R-module R1-free R1-separable groups rank reflexive regular cardinal Reid class result satisfies Shelah short exact sequence slender stationary set stationary subset strongly k-free submodule Suppose surjective Theorem topology torsion torsion-free torsionless ultrafilter uncountable cardinal W-group w-measurable weakly compact Whitehead group X-system

### Popular passages

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...