Dedekind factorization theorem
= Dedekind factorization theorem
{c}
If $\mathcal O_K=\mathbb Z[\theta]$ and the minimal polynomial of $\theta$ factors modulo a rational prime $p$ as
$$
\overline f=\prod_i\overline g_i^{e_i},
$$
then
$$
(p)=\prod_i(p,g_i(\theta))^{e_i},
$$
and the prime ideal $(p,g_i(\theta))$ has norm $p^{\deg g_i}$.
This gives an explicit instance of <unique factorization of ideals in a number field>.