Es sei p {\displaystyle {}p} eine Primzahl. Wir betrachten die Unterkörper der komplexen Zahlen, K = Q [ p , i ] {\displaystyle {}K=\mathbb {Q} [{\sqrt {p}},{\mathrm {i} }]} und L = Q [ p , − p ] {\displaystyle {}L=\mathbb {Q} [{\sqrt {p}},{\sqrt {-p}}]} . Zeige K = L {\displaystyle {}K=L} .
![{\displaystyle {}K=\mathbb {Q} [{\sqrt {p}},{\mathrm {i} }]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/39028a83caaa0f24991acaa01f512103c84b162a)
![{\displaystyle {}L=\mathbb {Q} [{\sqrt {p}},{\sqrt {-p}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aa946207388d96931cb62bbb90c6003fe57b67a6)
