show · nf.ramified_primes all knowls · up · search:

A prime integer $p$ is a ramified prime of a number field $K$ if, when the ideal generated by $p$ is factored into prime ideals in the ring of integers $\mathcal{O}_K$ of $K$, $$p\mathcal{O}_K= \mathcal{P_1}^{e_1}\cdots \mathcal{P_k}^{e_k},$$
there is an $i$ such that $e_i\geq 2$.

The ramified primes of $K$ are the primes dividing the discriminant of $K$.

Knowl status:
  • Review status: reviewed
  • Last edited by John Jones on 2018-03-20 18:02:02
Referred to by:
History: (expand/hide all)