Let B be a finitely generated
integral domain over a Noetherian domain A. The first theorem shows that
there are only finitely many imbedded prime divisors of principal ideals in B
if and only if this holds in A. The second theorem gives a necessary and
sufficient condition in order that only finitely many height one prime ideals in A
ramify in B, when A is locally factorial. The third theorem characterizes local
domains which contain infinitely many imbedded prime divisors of principal
ideals.