Definition:Prime Ideal of Number Field

Definition
Let $K$ be a number field.

Let $\mathcal O_K$ be its ring of integers.

Let $\mathfrak p \subseteq \mathcal O_K$ be an ideal.

Then $\mathfrak p$ is a prime ideal it is not the unit ideal $(1)$ and $\mathfrak p$ has no divisors other than $\mathfrak p$ and $(1)$.

Generalizations

 * Definition:Prime Ideal of Ring