Question

$F\subseteq E\subseteq M$ is finite field extensions, if $M/F$ is normal then $M/E$ is normal

score 47 · Answer 1 · 2019-05-05 14:51:48

47

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$F\subseteq E\subseteq M$ is finite field extensions, if $M/F$ is normal then $M/E$ is normal

Published on 05 May 2019 - 14:51

score 399 · Answer 2 · 2019-06-06 19:01:45

399

Views

How to see that $M$ is Galois over $k$ in Lang's proof that solvable extensions are a distinguished class? (Prop. VI.7.1, Algebra)

Published on 06 Jun 2019 - 19:01

score 1k · Answer 3 · 2014-11-09 10:13:35

1k

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If $F/k$ normal, $g,h \in F[X]$ monic irreducible factors of $f \in k[X]$, then $\exists\ \sigma \in Aut(F/k)$ s.t. $g^\sigma = h$.

Published on 09 Nov 2014 - 10:13

score 105 · Answer 4 · 2019-11-10 13:37:27

105

Views

Showing $K(\sqrt[3]{t}) / K$ is a normal extension.

Published on 10 Nov 2019 - 13:37

score 437 · Answer 5 · 2020-04-01 09:45:45

437

Views

A generalization of the theorem on natural irrationalities?

Published on 01 Apr 2020 - 9:45

score 61 · Answer 6 · 2020-04-01 19:51:01

61

Views

When is it true that $K \cap F(a) = F$ and $[K(a):F(a)] = [K:F]$?

Published on 01 Apr 2020 - 19:51

score 214 · Answer 7 · 2020-04-14 13:02:51

214

Views

Every algebraic extension of a finite field is a finite extension. True or False?

Published on 14 Apr 2020 - 13:02

score 234 · Answer 8 · 2020-06-04 15:58:56

234

Views

Restriction of the Frobenius automorphism for normal extensions

Published on 04 Jun 2020 - 15:58

score 65 · Answer 9 · 2020-07-29 19:34:09

65

Views

A problem to show that a certain field extension is not normal

Published on 29 Jul 2020 - 19:34

score 2.2k · Answer 10 · 2017-02-09 03:52:35

2.2k

Views

In a normal extension of a field, is there an automorphism that maps irreducible factors of a certain irreducible polynomial?

Published on 09 Feb 2017 - 3:52

score 181 · Answer 11 · 2017-03-19 06:39:04

181

Views

A finite extension of a normal extension is normal?

Published on 19 Mar 2017 - 6:39

score 126 · Answer 12 · 2026-02-22 19:55:09

126

Views

A statement about normal basis element , trace and characteristic of field

Published on 22 Feb 2026 - 19:55

score 84 · Answer 13 · 2023-02-10 00:48:31

84

Views

Tietze Extension Theorem - Munkres Section 35, Theorem 35.1

Published on 10 Feb 2023 - 0:48

score 95 · Answer 14 · 2023-03-10 00:58:56

95

Views

For field extension $M/L/K$ with $M/K$ normal, if $\sigma\in\mathrm{Aut}(M/K)$ implies $\sigma(L)\subset M^{\mathrm{Aut}(M/L)}$, must $L/K$ be normal?

Published on 10 Mar 2023 - 0:58

score 93 · Answer 15 · 2023-05-30 17:22:16

93

Views

Finite normal and separable extension

Published on 30 May 2023 - 17:22

List Question

$F\subseteq E\subseteq M$ is finite field extensions, if $M/F$ is normal then $M/E$ is normal

How to see that $M$ is Galois over $k$ in Lang's proof that solvable extensions are a distinguished class? (Prop. VI.7.1, Algebra)

If $F/k$ normal, $g,h \in F[X]$ monic irreducible factors of $f \in k[X]$, then $\exists\ \sigma \in Aut(F/k)$ s.t. $g^\sigma = h$.

Showing $K(\sqrt[3]{t}) / K$ is a normal extension.

A generalization of the theorem on natural irrationalities?

When is it true that $K \cap F(a) = F$ and $[K(a):F(a)] = [K:F]$?

Every algebraic extension of a finite field is a finite extension. True or False?

Restriction of the Frobenius automorphism for normal extensions

A problem to show that a certain field extension is not normal

In a normal extension of a field, is there an automorphism that maps irreducible factors of a certain irreducible polynomial?

A finite extension of a normal extension is normal?

A statement about normal basis element , trace and characteristic of field

Tietze Extension Theorem - Munkres Section 35, Theorem 35.1

For field extension $M/L/K$ with $M/K$ normal, if $\sigma\in\mathrm{Aut}(M/K)$ implies $\sigma(L)\subset M^{\mathrm{Aut}(M/L)}$, must $L/K$ be normal?

Finite normal and separable extension

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