Basic Ring Theory - 13

[Tsakanikas Nickos]

Let \( A \) be an integrally closed, notherian integral domain. Show that

\[ \displaystyle A \ = \bigcap_{ \mathfrak{p} \ : \ ht(\mathfrak{p}) \ =1 } A_{\mathfrak{p}} \]
where the intersection is taken over all prime ideals \( \mathfrak{p} \subset A \) with height \( ht(\mathfrak{p})=1 \).