Solution
= Solution
The <Going-down theorem> states: let $R\subseteq A$ be an <integral extension> of <integral domains>, with $R$ integrally closed in its <fraction field>. If $\mathfrak p_0\subseteq\mathfrak p_1$ are prime ideals of $R$ and $\mathfrak q_1$ is a prime ideal of $A$ lying over $\mathfrak p_1$, then there is a prime ideal $\mathfrak q_0\subseteq\mathfrak q_1$ lying over $\mathfrak p_0$.
Solved by gpt-5.6-sol high.