OVERRINGS OF HALF-FACTORIAL DOMAINS .2.

An atomic integral domain D is a half-factorial domain (HFD) if for an y irreducible elements alpha(1),...,alpha(n),beta 1,...,beta(m) of D w ith alpha 1...alpha(n) = beta(1)...beta(m), then n = m. We explore som e general properties of an integral domain D for which each localizati on of D is a HFD. In [5], we constructed an example of a Dedekind doma in with divisor class group II6 which is a HFD, but with a localizatio n which is not a HFD. We show that this construction can be extended t o the case where the divisor class group of D is any finite abelian gr oup except 1) cyclic p-groups, and 2) direct sums of copies of II2. We close with a look at the relationship between the elasticity of an at omic domain and the elasticity of its localizations.