A characterization ofnon-Noetherian BFDs and FFDs

Abstract

Characterizations of bounded and finite factorization domains are given using topological notions. Using our characterizations, the almost Dedekind domain and Prüfer domain constructed by Grams [3] are shown to be a BFD and an FFD, respectively. For a class of almost Dedekind (not Dedekind) domains it is shown that satisfying the ascending chain condition for principal ideals implies BFD.