Question

Normal closure as the compositum of conjugates

score 127 · Answer 1 · 2021-05-26 04:15:04

127

Views

Normal closure as the compositum of conjugates

Published on 26 May 2021 - 4:15

score 55 · Answer 2 · 2021-07-09 11:55:38

55

Views

Prove that $\Bbb{Q}(\sqrt2,\sqrt3,u)|_\Bbb{Q}$ is normal where $u^2=(9-5\sqrt3)(2-\sqrt2)$

Published on 09 Jul 2021 - 11:55

score 179 · Answer 3 · 2021-07-15 16:36:10

179

Views

Irreducible polynomial over normal extension

Published on 15 Jul 2021 - 16:36

score 103 · Answer 4 · 2021-07-16 18:39:43

103

Views

Splitting Field of $x^6-3x^4+3x^2-3$ \ Normal Extension \ Subfields

Published on 16 Jul 2021 - 18:39

score 163 · Answer 5 · 2021-08-03 15:50:23

163

Views

$L$ be an algebraically closed field and $\sigma \in \operatorname{Aut}(L)$, if $F=L^{\sigma}$, then every finite extension $E/F$ is cyclic.

Published on 03 Aug 2021 - 15:50

score 849 · Answer 6 · 2021-08-27 21:16:16

849

Views

Prove that $\mathbb{Q}(\sqrt{2+\sqrt{2}}) / \mathbb{Q}$ is a normal extension

Published on 27 Aug 2021 - 21:16

score 351 · Answer 7 · 2021-09-04 02:29:48

351

Views

Compositum of normal extensions

Published on 04 Sep 2021 - 2:29

score 98 · Answer 8 · 2021-09-10 16:35:36

98

Views

galois automorphism and normal (extension) of normal is normal

Published on 10 Sep 2021 - 16:35

score 50 · Answer 9 · 2021-09-19 10:58:34

50

Views

Extended automorphisms

Published on 19 Sep 2021 - 10:58

score 25 · Answer 10 · 2021-11-07 18:19:01

25

Views

If $K \subset L \subset \overline{L}=\overline{K}$, then is it true that $\sigma\in Aut(\overline{L}\mid K)$ satisfies $\sigma|_L\in Aut(L\mid K)$?

Published on 07 Nov 2021 - 18:19

score 50 · Answer 11 · 2021-11-09 09:28:42

50

Views

If $G=\mathsf{Aut}_k(F)$ acts on field $F$ algebraic over $k$ then do we have: orbit $G\alpha=\text{ roots of minimal polynomial of }\alpha$?

Published on 09 Nov 2021 - 9:28

score 100 · Answer 12 · 2021-11-14 17:00:04

100

Views

On normal extension, a square root of discriminant is in field F?

Published on 14 Nov 2021 - 17:00

score 71 · Answer 13 · 2022-01-13 11:05:06

71

Views

Is $F\hat{E_s}/E$ normal, where $F/E$ is a finite field extension?

Published on 13 Jan 2022 - 11:05

score 57 · Answer 14 · 2022-02-13 16:36:57

57

Views

Can someone explain me what they did in the proof that every extension of degree 2 is normal?

Published on 13 Feb 2022 - 16:36

score 157 · Answer 15 · 2022-02-16 19:02:28

157

Views

What does it mean that a normal extension remain normal under lifting?

Published on 16 Feb 2022 - 19:02

List Question

Normal closure as the compositum of conjugates

Prove that $\Bbb{Q}(\sqrt2,\sqrt3,u)|_\Bbb{Q}$ is normal where $u^2=(9-5\sqrt3)(2-\sqrt2)$

Irreducible polynomial over normal extension

Splitting Field of $x^6-3x^4+3x^2-3$ \ Normal Extension \ Subfields

$L$ be an algebraically closed field and $\sigma \in \operatorname{Aut}(L)$, if $F=L^{\sigma}$, then every finite extension $E/F$ is cyclic.

Prove that $\mathbb{Q}(\sqrt{2+\sqrt{2}}) / \mathbb{Q}$ is a normal extension

Compositum of normal extensions

galois automorphism and normal (extension) of normal is normal

Extended automorphisms

If $K \subset L \subset \overline{L}=\overline{K}$, then is it true that $\sigma\in Aut(\overline{L}\mid K)$ satisfies $\sigma|_L\in Aut(L\mid K)$?

If $G=\mathsf{Aut}_k(F)$ acts on field $F$ algebraic over $k$ then do we have: orbit $G\alpha=\text{ roots of minimal polynomial of }\alpha$?

On normal extension, a square root of discriminant is in field F?

Is $F\hat{E_s}/E$ normal, where $F/E$ is a finite field extension?

Can someone explain me what they did in the proof that every extension of degree 2 is normal?

What does it mean that a normal extension remain normal under lifting?

Trending Questions

Popular # Hahtags

Popular Questions