Question

Verify fundamental theorem of Galois for splitting field of $X^4\pm2\in\mathbb {Q}[X]$

score 172 · Answer 1 · 2026-03-26 21:14:03

172

Views

Verify fundamental theorem of Galois for splitting field of $X^4\pm2\in\mathbb {Q}[X]$

Published on 26 Mar 2026 - 21:14

score 189 · Answer 2 · 2026-03-26 21:14:05

189

Views

Galois correspondence of subgroups of $D_4$ with subfields of $\mathbb Q (\sqrt[4]{2},i)$

Published on 26 Mar 2026 - 21:14

score 114 · Answer 3 · 2020-06-17 23:24:04

114

Views

For Galois extension $L:K$, does $L = K(\alpha)$ imply $\{\sigma_1(\alpha), \dots, \sigma_n(\alpha)\}$ is a basis for $L$ over $K$?

Published on 17 Jun 2020 - 23:24

score 650 · Answer 4 · 2020-06-18 15:11:49

650

Views

What is the Galois group of $(x^3-2)(x^3-3)$ over $\mathbb{Q}$?

Published on 18 Jun 2020 - 15:11

score 212 · Answer 5 · 2026-03-27 02:40:27

212

Views

Group cohomology of Galois group of finite extension of finite fields

Published on 27 Mar 2026 - 2:40

score 353 · Answer 6 · 2020-06-20 16:52:03

353

Views

Galois Theory without the Primitive Element Theorem

Published on 20 Jun 2020 - 16:52

score 52 · Answer 7 · 2026-03-27 21:05:43

52

Views

How to express a field L in the form $M(\sqrt{d})$?

Published on 27 Mar 2026 - 21:05

score 345 · Answer 8 · 2020-06-20 19:21:39

345

Views

How to express the field $\mathbb Q(\sqrt[3]{2},\sqrt[3]{3})$ as a simple extension of $\mathbb Q$?

Published on 20 Jun 2020 - 19:21

score 37 · Answer 9 · 2026-02-23 06:40:31

37

Views

All roots of a polynomial in ring $F_2+uF_2+u^2F_2$, where $u^3=0$

Published on 23 Feb 2026 - 6:40

score 1.3k · Answer 10 · 2020-06-30 05:50:03

1.3k

Views

Proof of : If $K$ is a finite extension of $F$, then $o(G(K,F)) \leq [K:F]$

Published on 30 Jun 2020 - 5:50

score 37 · Answer 11 · 2020-06-30 06:04:08

37

Views

Abelian extensions $E|F$ and $F|K$ $\implies E|K$?

Published on 30 Jun 2020 - 6:04

score 1.2k · Answer 12 · 2020-06-30 06:30:29

1.2k

Views

What is the intuition behind mapping of elements from $GF(2^8)$ to $GF(((2^2)^2)^2)$?

Published on 30 Jun 2020 - 6:30

score 140 · Answer 13 · 2020-07-13 23:05:24

140

Views

Non Abelian Normal Field Extension with Abelian Subextensions

Published on 13 Jul 2020 - 23:05

score 44 · Answer 14 · 2020-07-15 14:48:38

44

Views

Lemma about certain extension of a Galois automorphism

Published on 15 Jul 2020 - 14:48

score 61 · Answer 15 · 2020-07-16 05:52:07

61

Views

Cyclic Field Extensions of sum of radicals

Published on 16 Jul 2020 - 5:52

List Question

Verify fundamental theorem of Galois for splitting field of $X^4\pm2\in\mathbb {Q}[X]$

Galois correspondence of subgroups of $D_4$ with subfields of $\mathbb Q (\sqrt[4]{2},i)$

For Galois extension $L:K$, does $L = K(\alpha)$ imply $\{\sigma_1(\alpha), \dots, \sigma_n(\alpha)\}$ is a basis for $L$ over $K$?

What is the Galois group of $(x^3-2)(x^3-3)$ over $\mathbb{Q}$?

Group cohomology of Galois group of finite extension of finite fields

Galois Theory without the Primitive Element Theorem

How to express a field L in the form $M(\sqrt{d})$?

How to express the field $\mathbb Q(\sqrt[3]{2},\sqrt[3]{3})$ as a simple extension of $\mathbb Q$?

All roots of a polynomial in ring $F_2+uF_2+u^2F_2$, where $u^3=0$

Proof of : If $K$ is a finite extension of $F$, then $o(G(K,F)) \leq [K:F]$

Abelian extensions $E|F$ and $F|K$ $\implies E|K$?

What is the intuition behind mapping of elements from $GF(2^8)$ to $GF(((2^2)^2)^2)$?

Non Abelian Normal Field Extension with Abelian Subextensions

Lemma about certain extension of a Galois automorphism

Cyclic Field Extensions of sum of radicals

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