## Groups of Divisibility |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

INTRODUCTION | 1 |

1 PARTIALLYORDERED GROUPS | 5 |

2 GROUPS OF DIVISIBILITY | 13 |

3 BASIC PROPERTIES OF dGROUPS | 22 |

4 dCONVEX SUBGROUPS | 28 |

5 VALUATIONS OF dGROUPS | 36 |

6 APPROXIMATION THEOREMS | 48 |

7 REALIZATION OF GROUPS OF DIVISIBILITY | 87 |

8 JAFFARDOHMs THEOREM | 96 |

9 EXACT SEQUENCES OF GROUPS OF DIVISIBILITY | 112 |

10 GROUPS OF DIVISIBILITY OF KRULL DOMAINS | 120 |

11 TOPOLOGICAL GROUPS OF DIVISIBILITY | 130 |

12 APPLICATIONS OF GROUPS OF DIVISIBILITY | 149 |

13 GENERALIZATIONS OF SEMIVALUATIONS | 163 |

REFERENCES | 172 |

SUBJECT INDEX | 180 |

### Common terms and phrases

Analogously approximation theorem Bezout domain bijection canonical map commutative complete integral closure construction contradiction Conversely convex subgroup d-convex d-group G d-homomorphism d-valuation Dedekind domain denote diagram directed d-group element of G example fact factor group following proposition following theorem functor GCD-domain Gilmer group G group of divisibility Heinzer Hence homomorphism ideal of G implies integral domain integrally closed irreducible isomorphism J.Math Jaffard Krull domain LEMMA Let G let H lex-exact m-ideal of G+ m-ring Math maximal ideal Moreover morphism multivalued addition natural transformation o-epimorphism o-ideal o-isomorphism obtain ordered groups partially ordered partially ordered set po-group G possible to show presheaf Priifer prime ideal Proof properties quotient field realization Ribenboim Schreier domain semigroup semivaluation sequence sheaf Skula subgroup H subgroup of G subset suppose theory of divisors topological field topological group totally ordered v-system valuation domain valuation ring value group