# 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 if and only if it is not the unit ideal $(1)$ and $\mathfrak p$ has no divisors other than $\mathfrak p$ and $(1)$.