Definition:Prime Ideal of Number Field

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

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