The following result was proved in [5,Remark 2.2].
Theorem 0.1. If R T are Noetherian rings such that there does not
exist any integrally dependent adjacent Noetherian rings between them, then
for each ¯c/¯b 2 T/Z ...
In this note, we show that a part of Ratliff (Proc Am Math Soc 101(3):395–402, 1987, Remark 2.2) is not correct. Some conditions are given under which the same holds.