  In this paper we exhibit an example of a three-dimensional regular local
domain (A, n) having a height-two prime ideal P with the property that the
extension PA^ of P to the n-adic completion A^ of A is not integrally closed.
We use a construction we have studied in earlier papers: For R=k[x,y,z], where
k is a field of characteristic zero and x,y,z are indeterminates over k, the
example A is an intersection of the localization of the power series ring
k[y,z][[x]] at the maximal ideal (x,y,z) with the field k(x,y,z,f, g) where f,
g are elements of (x,y,z)k[y,z][[x]] that are algebraically independent over
k(x,y,z). The elements f, g are chosen in such a way that using results from
our earlier papers A is Noetherian and it is possible to describe A as a nested
union of rings associated to A that are localized polynomial rings over k in
five variables.
