Factoring Ideals in Prüfer Domains

Abstract

We show that in certain Prüfer domains, each nonzero ideal $I$ can be factored as $I=I^v\Pi$, where $I^v$ is the divisorial closure of $I$ and $\Pi$ is a product of maximal ideals. This is always possible when the Prüfer domain is $h$-local, and in this case such factorizations have certain uniqueness properties. This leads to new characterizations of the $h$-local property in Prüfer domains. We also explore consequences of these factorizations and give illustrative examples.