Question

Does $[KL:L]=[K:K\cap L]$ when $L/(K\cap L)$ is normal?

score 55 · Answer 1 · 2023-06-17 20:31:34

55

Views

Does $[KL:L]=[K:K\cap L]$ when $L/(K\cap L)$ is normal?

Published on 17 Jun 2023 - 20:31

score 59 · Answer 2 · 2023-07-06 17:51:50

59

Views

Show $\mathbb{Q}(\sqrt{3+\sqrt{3}})/\mathbb{Q}$ is not a normal extension and find it's normal closure

Published on 06 Jul 2023 - 17:51

score 51 · Answer 3 · 2023-07-08 08:18:19

51

Views

Profinite topology on a Galois group can also be induced by normal finite intermediate extensions.

Published on 08 Jul 2023 - 8:18

score 119 · Answer 4 · 2015-04-06 20:25:05

119

Views

Normal extension and action of automorphisms on factors

Published on 06 Apr 2015 - 20:25

score 90 · Answer 5 · 2017-04-21 15:50:22

90

Views

For which rational values of $a$ is $\mathbb{Q}(\sqrt{\sqrt{5} + a}) / \mathbb{Q}$ a normal extension?

Published on 21 Apr 2017 - 15:50

score 113 · Answer 6 · 2017-04-25 07:09:29

113

Views

$L/k$ finite extension , $L_1,L_2 $ subfields of $L$ containing $k$ , $L_1/k$ separable and $L_2/k$ normal , then $[L_1L_2:L_2]=[L_1:L_1\cap L_2]$ ?

Published on 25 Apr 2017 - 7:09

score 278 · Answer 7 · 2017-04-25 16:26:28

278

Views

$c$ be algebraic , constructible over $\mathbb Q$ , $N$ be the normal closure of $\mathbb Q(c)/\mathbb Q$ ; then $[N:Q]$ is a power of $2$?

Published on 25 Apr 2017 - 16:26

score 383 · Answer 8 · 2017-05-08 11:19:42

383

Views

Totally transcendental extension and irreducibility.

Published on 08 May 2017 - 11:19

score 308 · Answer 9 · 2017-05-21 09:38:55

308

Views

How to determine whether an extension is normal extension.

Published on 21 May 2017 - 9:38

score 306 · Answer 10 · 2017-05-26 08:52:28

306

Views

Questions regarding tower of normal/separable extensions

Published on 26 May 2017 - 8:52

score 197 · Answer 11 · 2017-06-10 16:31:26

197

Views

Kaplansky's vs common definition of normal field extension

Published on 10 Jun 2017 - 16:31

score 106 · Answer 12 · 2017-09-14 09:40:54

106

Views

Is there a polynomial over $\mathbb{Q}$ which $K$ is its splitting field.

Published on 14 Sep 2017 - 9:40

score 549 · Answer 13 · 2017-10-09 19:22:15

549

Views

"Intersection" of separable subfields

Published on 09 Oct 2017 - 19:22

score 313 · Answer 14 · 2017-10-27 19:47:35

313

Views

If $E/K$ is normal and $K \subseteq F \subseteq E$ then $E/F$ is normal.

Published on 27 Oct 2017 - 19:47

score 184 · Answer 15 · 2017-11-24 13:04:05

184

Views

Example of an extension where Normal of a Normal extension is Normal.

Published on 24 Nov 2017 - 13:04

List Question

Does $[KL:L]=[K:K\cap L]$ when $L/(K\cap L)$ is normal?

Show $\mathbb{Q}(\sqrt{3+\sqrt{3}})/\mathbb{Q}$ is not a normal extension and find it's normal closure

Profinite topology on a Galois group can also be induced by normal finite intermediate extensions.

Normal extension and action of automorphisms on factors

For which rational values of $a$ is $\mathbb{Q}(\sqrt{\sqrt{5} + a}) / \mathbb{Q}$ a normal extension?

$L/k$ finite extension , $L_1,L_2 $ subfields of $L$ containing $k$ , $L_1/k$ separable and $L_2/k$ normal , then $[L_1L_2:L_2]=[L_1:L_1\cap L_2]$ ?

$c$ be algebraic , constructible over $\mathbb Q$ , $N$ be the normal closure of $\mathbb Q(c)/\mathbb Q$ ; then $[N:Q]$ is a power of $2$?

Totally transcendental extension and irreducibility.

How to determine whether an extension is normal extension.

Questions regarding tower of normal/separable extensions

Kaplansky's vs common definition of normal field extension

Is there a polynomial over $\mathbb{Q}$ which $K$ is its splitting field.

"Intersection" of separable subfields

If $E/K$ is normal and $K \subseteq F \subseteq E$ then $E/F$ is normal.

Example of an extension where Normal of a Normal extension is Normal.

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