Physical Sciences and Mathematics Commons^™

Intermediate Rings Between A Local Domain And Its Completion, William Heinzer, Christel Rotthaus, Sylvia Wiegand

Nebraska Cooperative Fish and Wildlife Research Unit: Staff Publications

We consider the structure of certain intermediate domains between a local Noetherian domain Rand an ideal-adic completion R* of R that arise as the intersection of R* 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.