Boundary valuation domains

Abstract

A half factorial domain (HFD) R is an atomic domain where, for any collection of irreducibles { α 1, α 2,…, α m , β 1, β 2,…, β n }, with α 1 α 2⋯ α m = β 1 β 2⋯ β n 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 HFD's—called boundary valuation domains—are defined and studied using this map.