  Suppose that $R$ is a local domain essentially of finite type over a field of
characteristic 0, and $\nu$ a valuation of the quotient field of $R$ which
dominates $R$. The rank of such a valuation often increases upon extending the
valuation to a valuation dominating $\hat R$, the completion of $R$. When the
rank of $\nu$ is 1, Cutkosky and Ghezzi handle this phenomenon by resolving the
prime ideal of infinite value, but give an example showing that when the rank
is greater than 1, there is no natural ideal in $\hat R$ that leads to this
obstruction. We extend their result on the resolution of prime ideals of
infinite value to valuations of arbitrary rank.
