Gluing minimal prime ideals in local rings
Gluing minimal prime ideals in local rings
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 C1,…,Cm. We show that there is a reduced local ring S⊆B with maximal ideal S∩M …