Question

Prove that $[\mathbb{Q}(\sqrt[4]{10}\zeta_8,i):\mathbb{Q}]=8$

score 179 · Answer 1 · 2026-03-26 01:28:39

179

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Prove that $[\mathbb{Q}(\sqrt[4]{10}\zeta_8,i):\mathbb{Q}]=8$

Published on 26 Mar 2026 - 1:28

score 939 · Answer 2 · 2026-03-26 17:32:55

939

Views

Tensor product of Galois extension

Published on 26 Mar 2026 - 17:32

score 226 · Answer 3 · 2019-04-21 01:44:48

226

Views

some questions on finding the Galois group of the splitting field of $x^4-3$

Published on 21 Apr 2019 - 1:44

score 154 · Answer 4 · 2019-04-21 04:33:32

154

Views

$\mathbb{Q}[\sqrt[3]{2}]/\mathbb{Q}$ is separable but not normal, $\mathbb{F}_p(T)/\mathbb{F}_p(T^p)$ is normal but not separable

Published on 21 Apr 2019 - 4:33

score 324 · Answer 5 · 2026-03-31 15:18:36

324

Views

Find degree of extension $Q$($\sqrt{1+\sqrt{-3}}$ + $\sqrt{1-\sqrt{-3}}$) over $Q$

Published on 31 Mar 2026 - 15:18

score 526 · Answer 6 · 2026-03-28 17:41:22

526

Views

A question about finite field extension of a finite field

Published on 28 Mar 2026 - 17:41

score 82 · Answer 7 · 2026-03-31 17:05:21

82

Views

A question on the Galois correspondance of $\sigma^2$ in $D_8$.

Published on 31 Mar 2026 - 17:05

score 73 · Answer 8 · 2026-03-28 17:40:25

73

Views

A question about the degree of an extension field

Published on 28 Mar 2026 - 17:40

score 563 · Answer 9 · 2026-03-28 08:35:37

563

Views

Automorphisms of the field of rational functions $\Bbb C(t)$

Published on 28 Mar 2026 - 8:35

score 192 · Answer 10 · 2026-03-25 01:17:11

192

Views

Does the abelianization of the Galois group determine the ideal class group?

Published on 25 Mar 2026 - 1:17

score 100 · Answer 11 · 2019-04-22 23:01:52

100

Views

Working on Galois Theory. Splitting field of f(x) = $x^2 + 11 \in Q[x]$

Published on 22 Apr 2019 - 23:01

score 65 · Answer 12 · 2026-03-28 17:42:07

65

Views

Finding the generator of a cyclic group

Published on 28 Mar 2026 - 17:42

score 892 · Answer 13 · 2026-03-20 08:21:46

892

Views

Let $K|F$ be a finite separable extension (algebraic), then show that $\operatorname{Tr}_{K|F} : K \to F$ is surjective.

Published on 20 Mar 2026 - 8:21

score 168 · Answer 14 · 2019-04-23 15:37:03

168

Views

Order of a non-normal Galois Group

Published on 23 Apr 2019 - 15:37

score 163 · Answer 15 · 2026-03-25 03:18:08

163

Views

The Relationship Between Cyclotomic Polynomials and Ramification

Published on 25 Mar 2026 - 3:18

List Question

Prove that $[\mathbb{Q}(\sqrt[4]{10}\zeta_8,i):\mathbb{Q}]=8$

Tensor product of Galois extension

some questions on finding the Galois group of the splitting field of $x^4-3$

$\mathbb{Q}[\sqrt[3]{2}]/\mathbb{Q}$ is separable but not normal, $\mathbb{F}_p(T)/\mathbb{F}_p(T^p)$ is normal but not separable

Find degree of extension $Q$($\sqrt{1+\sqrt{-3}}$ + $\sqrt{1-\sqrt{-3}}$) over $Q$

A question about finite field extension of a finite field

A question on the Galois correspondance of $\sigma^2$ in $D_8$.

A question about the degree of an extension field

Automorphisms of the field of rational functions $\Bbb C(t)$

Does the abelianization of the Galois group determine the ideal class group?

Working on Galois Theory. Splitting field of f(x) = $x^2 + 11 \in Q[x]$

Finding the generator of a cyclic group

Let $K|F$ be a finite separable extension (algebraic), then show that $\operatorname{Tr}_{K|F} : K \to F$ is surjective.

Order of a non-normal Galois Group

The Relationship Between Cyclotomic Polynomials and Ramification

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