I'm trying to prove that the ring of integers of $K=\mathbb{Q}(\sqrt7, \sqrt13)$ is not of the form $ \mathbb {Z}[a]$ for some $a$.
Unfortunately I can not figure out where to start. I tried to reason with the absurd, finding contradictions with the theorem Kummer-Dedekind but I did not find them. Is there someone that can to give me a detailed demonstration of this fact ? Many thanks to everyone who give me this help !