A **unramified (rational) prime** of a number field $K$ is a prime integer $p$ such that the ideal generated by $p$ is factored into distinct prime ideals in the ring of integers $\mathcal{O}_K$ of $K$ $$p\mathcal{O}_K = \mathcal{P}_1\cdots \mathcal{P}_k.$$

The unramified primes of $K$ are the primes which do not divide the discriminant of $K$.

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- Last edited by Alina Bucur on 2018-07-08 00:57:00

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- 2018-07-08 00:57:00 by Alina Bucur (Reviewed)