Some characterizations of Krull domains

AbstractIn this paper, we define the v-finiteness for a length function Lv on the set of all v-ideals of an integral domain R and show that R is a Krull domain if and only if every proper integral v-ideal of R has v-finite length and Lv((AB)v)=Lv(A)+Lv(B) for every pair of proper integral v-ideals A and B in R. We also give Euclidean-like characterizations of factorial, Krull, and π-domains. Finally we define the notion of quasi-∗-invertibility and show that if every proper prime t-ideal of an integral domain R is quasi-t-invertible, then R is a Krull domain