As is well known, if R is a ring in which every prime ideal is an intersection of primitive ideals, the same is true of R[X] . The purpose of this paper is to give a general theorem which shows that the above result remains true when rnany other classes of prime ideals are considered in place of prirnitive ideals.
Proceedings of the American Mathematical Society. Providence, RI. Vol. 105, no. 2 (feb. 1989), p. 281-286.