## Abelian GroupsThis volume contains information offered at the international conference held in Curacao, Netherlands Antilles. It presents the latest developments in the most active areas of abelian groups, particularly in torsion-free abelian groups.;For both researchers and graduate students, it reflects the current status of abelian group theory.;Abelian Groups discusses: finite rank Butler groups; almost completely decomposable groups; Butler groups of infinite rank; equivalence theorems for torsion-free groups; cotorsion groups; endomorphism algebras; and interactions of set theory and abelian groups.;This volume contains contributions from international experts. It is aimed at algebraists and logicians, research mathematicians, and advanced graduate students in these disciplines. |

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### Contents

Section 1 | 1 |

Section 2 | 43 |

Section 3 | 55 |

Section 4 | 65 |

Section 5 | 79 |

Section 6 | 97 |

Section 7 | 105 |

Section 8 | 111 |

Section 11 | 157 |

Section 12 | 175 |

Section 13 | 193 |

Section 14 | 201 |

Section 15 | 209 |

Section 16 | 219 |

Section 17 | 241 |

Section 18 | 247 |

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### Common terms and phrases

abelian groups Algebra application assume bound Butler groups called cardinality commutative completely decomposable groups Conference consequence consider construction contains Corollary countable critical decomposition define definition denote dimension direct sum divisible elements endomorphism equivalent exact example exists extension fact field finite rank flat Fuchs given Göbel group G height Hence ideal implies inclusion induced infinite injective integers invariants isomorphism left R-module Lemma Math Mathematics matrix minimal modules Moreover natural Note Observe obtain ordered particular poset presented prime problem projective Proof Proposition prove pure subgroup quasi-isomorphic question quotient regulating subgroup representation respectively result ring satisfies sequence space split strongly indecomposable structure submodule subset summand Suppose Theorem theory topology torsion torsion-free abelian groups torsion-free group typeset University valuation domain write