# integrally closed domain

• Aug 19th 2010, 11:46 PM
KaKa
integrally closed domain
"Let $A$ be an integrally closed noertherian domain. Then
$A=\cap_{ht(p)=1} A_p$, where the intersection is taken over all prime ideals of height $1$."

The above fact is true.
I want to find some counterexample when $A$ is not integrally closed.
Can you give it?