List questions from separable-extension

Published on 16 Nov 2017 - 20:19

237

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Simple extension is splitting field of $f=X^p-X+a \in K[X]$ with $char(K)=p$

Published on 05 Dec 2017 - 14:16

72

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If Gal(f/K) is simple then for each extension F/K, Gal(f/F) = Gal(f/K) or trivial.

Published on 15 Dec 2017 - 23:49

269

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If $Gal(f/\mathbb{Q}) \cong S_n$ then $Gal(f/\mathbb{Q}(\alpha_1)) \cong S_{n-1}$?

Published on 16 Dec 2017 - 14:08

1k

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$F/K$ finite extension, then $\exists !$ intermediate field $K \subset L \subset F$ such that $L/K$ separable and $F/L$ purely inseparable

Published on 11 Apr 2012 - 8:59

688

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How to calculate separable closures of an algebraic extension?

Published on 21 May 2012 - 16:30

1.2k

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Show that if $K \subset L$, then the separable closure of $K$ in $L$ is a field

Published on 29 Sep 2012 - 2:13

3.9k

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Ways of finding primitive element of separable extension $\Bbb{Q}(\sqrt[4]{2},i)$ over $\Bbb{Q}$.

Published on 15 Feb 2013 - 22:27

1k

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A problem on separable extension on field of characteristic $p>0$

Published on 31 Jul 2020 - 17:13

41

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familiy of polynomials separable

Published on 23 Feb 2026 - 8:57

219

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Examples of finite-dimensional, semisimple, non-separable $k$-algebras?

Published on 07 Aug 2020 - 12:09

152

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Certain separable ring extensions

Published on 25 Aug 2020 - 1:50

67

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Example of non-flat $R \subseteq R[w]$

Published on 17 Sep 2020 - 22:00

221

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Galois action on a tensor product of fields

Published on 28 Sep 2020 - 9:58

58

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Question related to separable extension.

Published on 15 Oct 2020 - 11:31

List Question

Does $L_1(w)=L_2(w)$ imply $L_1=L_2$?

Simple extension is splitting field of $f=X^p-X+a \in K[X]$ with $char(K)=p$

If Gal(f/K) is simple then for each extension F/K, Gal(f/F) = Gal(f/K) or trivial.

If $Gal(f/\mathbb{Q}) \cong S_n$ then $Gal(f/\mathbb{Q}(\alpha_1)) \cong S_{n-1}$?

$F/K$ finite extension, then $\exists !$ intermediate field $K \subset L \subset F$ such that $L/K$ separable and $F/L$ purely inseparable

How to calculate separable closures of an algebraic extension?

Show that if $K \subset L$, then the separable closure of $K$ in $L$ is a field

Ways of finding primitive element of separable extension $\Bbb{Q}(\sqrt[4]{2},i)$ over $\Bbb{Q}$.

A problem on separable extension on field of characteristic $p>0$

familiy of polynomials separable

Examples of finite-dimensional, semisimple, non-separable $k$-algebras?

Certain separable ring extensions

Example of non-flat $R \subseteq R[w]$

Galois action on a tensor product of fields

Question related to separable extension.

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