Half factorial domains

Abstract

LetR be a commutative domain with 1. We termR an HFD (Half-Factorial-Domain) provided the equality Π i=1 n χi=Π{f=1/m}y f impliesm=n, whenever thex’s and they’s are non-zero, non-unit and irreducible elements ofR. The purpose of this note is to study HFD’s, in particular, Krull domains that are HFD’s, and to provide examples of HFD’s, that contradict a conjecture of Narkiewicz.