No abstract

No abstract

No abstract

Let B be a reduced local (Noetherian) ring with maximal ideal M . Suppose that B contains the rationals, B/M is uncountable and |B| = |B/M |. Let the minimal prime ideals of B be partitioned into m ≥ 1 subcollections C 1 , . . . , C m . We show that there is a reduced local ring S ⊆ B with maximal ideal S ∩ M 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 P ∩ S = Q ∩ S if and only if P and Q are in C i for some i = 1, 2, . . . , m.

No abstract