Intermediate rings between a local domain and its completion

Abstract

We consider the structure of certain intermediate domains betweena local Noetherian domain $R$ and an ideal-adic completion $R^{\ast}$ of $R$ that arise as the intersection of $R^{\ast}$ with a field containing $R$. In the case where the intersection domain $A$ can be expressed as a directed union of localized polynomial extension rings of $R$, the computation of $A$ is easier. We examine conditions for this to happen. We also present examples to motivate and illustrate the concepts considered.