IDEAL FACTORIZATION IN STRONGLY DISCRETE INDEPENDENT RINGS OF KRULL TYPE, II

Abstract

A ZPUI domain $D$ is an integral domain with property $(\mathrm{\#})$: every nonzero proper ideal $I$ of $D$ can be written as $I=J{P}_1\cdots P_n$, where $J$ is an invertible ideal of $D$ and $\{P_1,\dots ,P_n\}$ is a nonempty collection of pairwise comaximal prime ideals of $D$. Among other things, we study two types of natural generalizations of ZPUI domains: (i) the $J$ in the property $(\mathrm{\#})$ is principal and (ii) the property $(\mathrm{\#})$ holds for all nonzero principal ideals of $D$. For example, we show that (1) $D$ satisfies (i) if and only if $D$ is a ZPUI domain whose invertible ideals are principal and (2) $D$ satisfies (ii) if and only if $D$ is an $h$-local domain in which each maximal ideal is invertible. We also study the $w$-operation analogs of these two properties.