Nebraska Cooperative Fish & Wildlife Research Unit


Date of this Version

Spring 1999


1999 by the Board of Trustees of the University of Illinois Manufactured in the United States of America


ILLINOIS JOURNAL OF MATHEMATICS Volume 43, Number I, Spring 1999


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.