Theorem 10.5. Assuming that:

$O_{K}$ , $O_{L}$ , $K$ , $L$ as usual
for $p$ a non-zero prime ideal of $O_{K}$ , we write $p O_{L} P_{1}^{e_{1}} \dots P_{r}^{e_{r}}$

L

extending

| ∙ |_{p}

(up to equivalence) are precisely

| ∙ |_{P_{1}}, \dots, | ∙ |_{P_{L}}