Gluing minimal prime ideals in local rings

Abstract

Let B be a reduced local (Noetherian) ring with maximal ideal M. Suppose that B contains the rationals, B/M is uncountable and Let the minimal prime ideals of B be partitioned into subcollections We show that there is a reduced local ring with maximal ideal such that the completion of S with respect to its maximal ideal is isomorphic to the completion of B with respect to its maximal ideal and such that, if P and Q are prime ideals of B, then if and only if P and Q are in Ci for some