Question

Degree of extension $\mathbb{C}/K$, where $K$ is maximal with the property $\sqrt{2} \notin K$

score 99 · Answer 1 · 2020-05-23 05:05:03

99

Views

Degree of extension $\mathbb{C}/K$, where $K$ is maximal with the property $\sqrt{2} \notin K$

Published on 23 May 2020 - 5:05

score 48 · Answer 2 · 2020-05-23 22:35:28

48

Views

Is $\operatorname{Gal}(\overline{\mathbb{F}_p} \,/\, \mathbb{F}_p)$ cyclic?

Published on 23 May 2020 - 22:35

score 186 · Answer 3 · 2020-05-26 19:52:00

186

Views

Intuition for equivalent definitions of Galois extension

Published on 26 May 2020 - 19:52

score 249 · Answer 4 · 2020-05-30 19:32:54

249

Views

Galois group of $x^6-2x^4+2x^2-2$ over $\mathbb{Q}$

Published on 30 May 2020 - 19:32

score 251 · Answer 5 · 2026-03-25 09:29:14

251

Views

Relation between subgroup topology and Krull topology for an intermediate field of a Galois extension

Published on 25 Mar 2026 - 9:29

score 162 · Answer 6 · 2020-05-31 20:19:15

162

Views

An extension corresponding to a subgroup of Galois group

Published on 31 May 2020 - 20:19

score 68 · Answer 7 · 2020-06-02 22:43:28

68

Views

Decomposition group does not depend on the prime

Published on 02 Jun 2020 - 22:43

score 36 · Answer 8 · 2020-06-02 23:00:54

36

Views

Prime inert in each subfields never occurs

Published on 02 Jun 2020 - 23:00

score 101 · Answer 9 · 2020-06-03 22:13:06

101

Views

Find Galois group of $\mathbb{Q}\sqrt{(2+\sqrt2)(3+\sqrt3)}$

Published on 03 Jun 2020 - 22:13

score 281 · Answer 10 · 2020-06-04 16:09:03

281

Views

Description of the decomposition and the inertia group in terms of the product $\mathbb{Z}^_{p^k}\times \mathbb{Z}^_n $

Published on 04 Jun 2020 - 16:09

score 258 · Answer 11 · 2020-06-04 17:40:37

258

Views

Splitting of primes and other properties of $\mathbb{Q}[\omega]$ for $\omega=e^{2\pi i/m}$

Published on 04 Jun 2020 - 17:40

score 102 · Answer 12 · 2020-06-06 14:55:09

102

Views

Let $X = \{ \sqrt{p} : p \text{ is prime} \}$, $Y \subseteq X$ and $\sqrt{p} \not\in Y$. Show that $[\mathbb{Q}(Y)(\sqrt{p}) : \mathbb{Q}(Y)] = 2$.

Published on 06 Jun 2020 - 14:55

score 162 · Answer 13 · 2020-06-08 16:40:24

162

Views

Criterion for completely splitting primes in a radical extension

Published on 08 Jun 2020 - 16:40

score 75 · Answer 14 · 2020-06-10 02:56:12

75

Views

Char $p$ fields, extension/subextension

Published on 10 Jun 2020 - 2:56

score 18 · Answer 15 · 2020-06-12 08:37:59

18

Views

Galois-property extends across different roots?

Published on 12 Jun 2020 - 8:37

List Question

Degree of extension $\mathbb{C}/K$, where $K$ is maximal with the property $\sqrt{2} \notin K$

Is $\operatorname{Gal}(\overline{\mathbb{F}_p} \,/\, \mathbb{F}_p)$ cyclic?

Intuition for equivalent definitions of Galois extension

Galois group of $x^6-2x^4+2x^2-2$ over $\mathbb{Q}$

Relation between subgroup topology and Krull topology for an intermediate field of a Galois extension

An extension corresponding to a subgroup of Galois group

Decomposition group does not depend on the prime

Prime inert in each subfields never occurs

Find Galois group of $\mathbb{Q}\sqrt{(2+\sqrt2)(3+\sqrt3)}$

Description of the decomposition and the inertia group in terms of the product $\mathbb{Z}^_{p^k}\times \mathbb{Z}^_n $

Splitting of primes and other properties of $\mathbb{Q}[\omega]$ for $\omega=e^{2\pi i/m}$

Let $X = \{ \sqrt{p} : p \text{ is prime} \}$, $Y \subseteq X$ and $\sqrt{p} \not\in Y$. Show that $[\mathbb{Q}(Y)(\sqrt{p}) : \mathbb{Q}(Y)] = 2$.

Criterion for completely splitting primes in a radical extension

Char $p$ fields, extension/subextension

Galois-property extends across different roots?

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