\begin{definition}[Definition:Prime Ideal of Number Field]
Let $K$ be a number field.
Let $\OO_K$ be its ring of integers.
Let $\mathfrak p \subseteq \OO_K$ be an ideal.
Then $\mathfrak p$ is a '''prime ideal''' {{iff}} it is not the unit ideal $\ideal 1$ and $\mathfrak p$ has no divisors other than $\mathfrak p$ and $\ideal 1$.
\end{definition}