Definition:Prime Ideal of Number Field

Definition
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 it is not the unit ideal $\ideal 1$ and $\mathfrak p$ has no divisors other than $\mathfrak p$ and $\ideal 1$.

Generalizations

 * Definition:Prime Ideal of Ring