How Far Is An HFD from A UFD?

Abstract In this paper, we study an invariant (R) introduced by Scott Chapman to measure how far an HFD R is from being a UFD. We show that if either R contains a prime element or R is a Krull domain with finite divisor class group, then R is a UFD if and only if (R) = 0. However, we give an example of an atomic integral domain R with (R) = 0 which is not an HFD.