Find the integers of degree 4 extension

Asked Dec 23 '21 at 20:01

Active Dec 23 '21 at 20:01

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So, I have been trying to solve the following problem: find the ring of integers in $\mathbb{Q}(\sqrt{3}+\sqrt{7}).$

Of course, the answer for $\mathbb{Q}(\sqrt{3})$ is clear as is for $\mathbb{Q}(\sqrt{7}),$ you just look for the residue modulo $4$ and you get the answer.

However, then I got stuck because I don't know how to derive an analogous criterion for quadratic extensions of $\mathbb{Q}(\sqrt{d}).$ Can anyone suggest an approach? Thank you!

asked Dec 23 '21 at 20:01

Grisha Taroyan

1

In Marcus book on number fields, the ring of integers in all biquadratic number fields is computed. Here $K=\Bbb Q(\sqrt3,\sqrt{7})$. On this site, several posts are actually related or even a duplicate. Start with this post. Also see here, why we have a biquadratic number field here. – Dietrich Burde Dec 23 '21 at 20:13
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Does this answer your question? On the ring of integers of a biquadratc number field. – Dietrich Burde Dec 23 '21 at 20:21

Find the integers of degree 4 extension

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