Solution
= Solution
If $Q\mid PO_L$, then $PO_L\subseteq Q$, so $P\subseteq Q\cap O_K$. The contraction is a nonzero prime <ideal> of $O_K$ containing the maximal <ideal> $P$, hence equals $P$. Conversely, if $P=Q\cap O_K$, every element of $P$ lies in $Q$, so the <ideal> it generates satisfies $PO_L\subseteq Q$, equivalently $Q\mid PO_L$.