We consider properties of extensions of Krull domains such as flatness that
involve behavior of extensions and contractions of prime ideals. Let (R,m) be
an excellent normal local domain with field of fractions K, let y be a nonzero
element in m, and let R* denote the (y)-adic completion of R. For a finite set
w of elements of yR* that are algebraically independent over R, we construct
two Krull domains: an intersection domain A that is the intersection of R* with
the field of fractions of K[w], and an approximation domain B to A. If R is
countable with dim R at least 2, we prove that there exist sets w as above such
that the extension R[w] to R*[1/y] is flat. In this case B = A is Noetherian,
but may fail to be excellent as we demonstrate with examples. We present
several theorems involving the construction. These theorems yield examples
where B is properly contained in A and A is Noetherian while B is not
Noetherian, and other examples where B = A is not Noetherian.Comment: 24 pages to appear in JPA