Overring of half-factorial domains. II

Abstract

An atomic integral domain D is a half-factorial domain (HFD) if for any irreducible elements α1,…,αn,β1,…,βmof D with α1,…,αn= β1,…,βm, then n = m. We explore some general properties of an integral domain D for which each localization of D is a HFD. In [5], we constructed an example of a Dedekind domain with divisor class group Z 6 which is a HFD, but with a localization which is not a HFD. We show that this construction can be extended to the case where the divisor class group of D is any finite abelian group except 1)cyclic p-group, and 2)direct sums of copies of Z 2. We close with a look at the relationship between the elasticity of an atomic domain and the elasticity of its localization.