query: Show that $\mathbb{Q}(\sqrt{2 +\sqrt{2}})$ is a cyclic quartic field i.e. is a galois extension of degree 4 with cyclic galois group
positive_passages.docid: 622
positive_passages.text: Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
negative_passages.docid: 111291
negative_passages.text: Galois group of $\mathbb Q(\sqrt{4+\sqrt 7})/\mathbb Q$
negative_passages.docid: 95563
negative_passages.text: Galois group of a biquadratic quartic
negative_passages.docid: 51021
negative_passages.text: Find all the intermediate fields of the splitting field of $x^4 - 2$ over $\mathbb{Q}$
negative_passages.docid: 132386
negative_passages.text: Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
negative_passages.docid: 50668
negative_passages.text: Show that $\mathbb{Q}(\sqrt2, \sqrt[3]2)$ is a primitive field extension of $\mathbb{Q}$.
negative_passages.docid: 63280
negative_passages.text: Show that the set $\mathbb{Q}[\sqrt{2}] = \{a + b \sqrt{2} \mid a, b \in \mathbb{Q}\}$ is a field with the usual multiplication and addition.
negative_passages.docid: 155771
negative_passages.text: Product of degree of two field extensions of prime degree
negative_passages.docid: 92517
negative_passages.text: Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
negative_passages.docid: 22632
negative_passages.text: Galois group of $x^4-2$
negative_passages.docid: 24168
negative_passages.text: A characterisation of quadratic extensions contained in cyclic extensions of degree 4
negative_passages.docid: 46730
negative_passages.text: How to show $\mathbb{Q}(\alpha^{4})=\mathbb{Q}(\alpha)$?
negative_passages.docid: 98803
negative_passages.text: Square roots of integers and cyclotomic fields
negative_passages.docid: 16163
negative_passages.text: Show $\mathbb{Q}(\sqrt{2},\sqrt{3})$ is a simple extension field of $\mathbb{Q}$.
negative_passages.docid: 146617
negative_passages.text: A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
negative_passages.docid: 142212
negative_passages.text: Let $q$ be a prime congruent to 3 mod 4, prove the quotient ring $\mathbb{Z}[i]/(q)$ is a field with $q^2$ elements
negative_passages.docid: 4996
negative_passages.text: Proving $Gal(K/\mathbb{Q})$ is $D_4$.