Question

Showing $\mathbb{Q}(\sqrt{5+2\sqrt{6}}) = \mathbb{Q}(\sqrt{2},\sqrt{3})$

score 141 · Answer 1 · 2026-03-25 12:37:35

141

Views

Showing $\mathbb{Q}(\sqrt{5+2\sqrt{6}}) = \mathbb{Q}(\sqrt{2},\sqrt{3})$

Published on 25 Mar 2026 - 12:37

score 224 · Answer 2 · 2026-04-01 04:33:45

224

Views

How many intermediate fields?

Published on 01 Apr 2026 - 4:33

score 238 · Answer 3 · 2026-03-28 04:35:20

238

Views

find $\alpha \in \mathbb{\overline{Q}}$ such that $\operatorname{Gal}(\mathbb{Q}(\alpha)/\mathbb{Q}) \cong \mathbb{Z}_5$

Published on 28 Mar 2026 - 4:35

score 143 · Answer 4 · 2026-03-25 03:22:45

143

Views

Why $p$th power are not allowed in radical extensions?

Published on 25 Mar 2026 - 3:22

score 374 · Answer 5 · 2019-08-14 19:33:36

374

Views

Normal extension $\Longleftrightarrow$ splitting field extension, intuitive or counterintuitive?

Published on 14 Aug 2019 - 19:33

score 85 · Answer 6 · 2019-08-17 15:59:44

85

Views

Galois group of order $n!$

Published on 17 Aug 2019 - 15:59

score 84 · Answer 7 · 2019-08-17 17:38:39

84

Views

Proof Explanation Field and Galois Theory

Published on 17 Aug 2019 - 17:38

score 304 · Answer 8 · 2019-08-18 22:16:51

304

Views

Galois Group of $\mathbb{Q}(\sqrt{\sqrt{3}-1})$

Published on 18 Aug 2019 - 22:16

score 251 · Answer 9 · 2026-03-26 19:02:04

251

Views

Is this a good summary of why $\int e^{x^2}\,dx$ doesn't exist in elementary form (using differential Galois theory)?

Published on 26 Mar 2026 - 19:02

score 57 · Answer 10 · 2026-03-29 17:33:57

57

Views

For any monic irreducible $f\in F[x]$ with $\deg(f)|[K:F]$, there is $\alpha \in K$ such that $m_{F}(\alpha)=f$

Published on 29 Mar 2026 - 17:33

score 166 · Answer 11 · 2019-08-25 14:04:11

166

Views

Proof that $\alpha$ is constructible $\iff$ there exists a finite tower of degree two extensions.

Published on 25 Aug 2019 - 14:04

score 213 · Answer 12 · 2026-03-25 16:46:25

213

Views

Why is $[\mathbb{Q}(\zeta):\mathbb{Q}] = 8$ and not $14$? (Where $\zeta$ is a primitive $15^{th}$ root of unity)

Published on 25 Mar 2026 - 16:46

score 109 · Answer 13 · 2019-08-28 04:27:03

109

Views

Can we find a Galois extension with Galois group $\mathbf{Z}$?

Published on 28 Aug 2019 - 4:27

score 89 · Answer 14 · 2019-08-28 15:11:36

89

Views

Degree of extension $\mathbb{Q}(\sqrt{3+2\sqrt{2}})$ over $\mathbb{Q}$

Published on 28 Aug 2019 - 15:11

score 157 · Answer 15 · 2026-02-23 04:55:09

157

Views

Finite dimensional field extension of Q simple

Published on 23 Feb 2026 - 4:55

List Question

Showing $\mathbb{Q}(\sqrt{5+2\sqrt{6}}) = \mathbb{Q}(\sqrt{2},\sqrt{3})$

How many intermediate fields?

find $\alpha \in \mathbb{\overline{Q}}$ such that $\operatorname{Gal}(\mathbb{Q}(\alpha)/\mathbb{Q}) \cong \mathbb{Z}_5$

Why $p$th power are not allowed in radical extensions?

Normal extension $\Longleftrightarrow$ splitting field extension, intuitive or counterintuitive?

Galois group of order $n!$

Proof Explanation Field and Galois Theory

Galois Group of $\mathbb{Q}(\sqrt{\sqrt{3}-1})$

Is this a good summary of why $\int e^{x^2}\,dx$ doesn't exist in elementary form (using differential Galois theory)?

For any monic irreducible $f\in F[x]$ with $\deg(f)|[K:F]$, there is $\alpha \in K$ such that $m_{F}(\alpha)=f$

Proof that $\alpha$ is constructible $\iff$ there exists a finite tower of degree two extensions.

Why is $[\mathbb{Q}(\zeta):\mathbb{Q}] = 8$ and not $14$? (Where $\zeta$ is a primitive $15^{th}$ root of unity)

Can we find a Galois extension with Galois group $\mathbf{Z}$?

Degree of extension $\mathbb{Q}(\sqrt{3+2\sqrt{2}})$ over $\mathbb{Q}$

Finite dimensional field extension of Q simple

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