A **prime** $\mathfrak p$ of a number field $K$ is a nonzero prime ideal of its ring of integers $\mathcal O_K$.

The ideal $\mathfrak p \cap\mathcal O_K$ is a nonzero prime ideal of $\Z$ (a prime of $\Q$), which is necessarily a principal ideal $(p)$ for some prime number $p$. The prime $\mathfrak p$ is then said to be a **prime above** $p$

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- Review status: beta
- Last edited by Andrew Sutherland on 2019-05-10 10:45:26

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