Abstract:
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 (where Z = Rad(T) = Rad(R) and ¯b, ¯c regular in R/Z),
we have either ¯c/¯b 2 R/Z or ¯ b/¯c 2 R/Z, and so (R/Z)[¯c/¯b] is a localization
of R/Z.