PRIME IDEALS LYING OVER ZERO IN POLYNOMIAL-RINGS

Let R be a Noetherian domain and x an indeterminate. Let P and Q be tw o finite sets of prime ideals in the polynomial ring R[x]. Necessary a nd sufficient conditions are given for the existence of a prime ideal K in R[x] such that K boolean AND R = O, K contains a monic polynomial , and K is contained in every prime ideal in P but not in any prime id eal in Q. (C) 1995 Academic Press, Inc.