Boundary valuation domains

A half factorial domain (HFD) R is an atomic domain where, for any collection of irreducibles {α1,α2,…,αm,β1,β2,…,βn}, with α1α2 αm=β1β2 βn we have n=m. In a paper by J. Coykendall [Comm. Algebra 27 (1999) 3153–3159], a generalization of the length function of Zaks [Israel J. Math. 37 (1980) 281–302], called the boundary map, was introduced. A new class of HFDʹs—called boundary valuation domains—are defined and studied using this map.