List questions from separable-extension

Published on 23 May 2021 - 12:37

96

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Theorem 17.22 from Ian Stewart's Galois Theory

Published on 25 May 2021 - 19:03

128

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Normal closure as the compositum of conjugates

Published on 23 Feb 2026 - 6:20

25

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Unseparable element becomes separable

Published on 27 May 2021 - 22:48

279

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Inseparable field extension of degree 2

Published on 01 Jun 2021 - 19:18

66

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How to reduce to the affine case? Number of points in the fibre and the degree of field extension.

Published on 07 Jun 2021 - 0:14

234

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Every algebraic extension of a finite field $F$ is separable

Published on 08 Jun 2021 - 22:13

185

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Is the proposition $[KL:L]=[K:F]$ iff $K\cap L=F$ for finite Galois extension still hold for separable extension?

Published on 11 Jun 2021 - 9:29

117

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Is every isogeny over $\mathbb Q$ separable?

Published on 23 Feb 2026 - 13:47

52

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Functional Analysis : A question abaout extensions without use the Banach Theorem or Zorn's lemma .

Published on 16 Jun 2021 - 16:52

111

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Equality between degree of separability of field extensions.

Published on 20 Jun 2021 - 13:16

279

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Is an algebraic extension of a separably closed field separably closed?

Published on 24 Jun 2021 - 15:57

146

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Let $K=F(u)$ be a separable extension of $F$ with $u^m\in F$. Show that if the characteristic of $F$ is $p$ and $m=p^tr$, then $u^r\in F$.

Published on 17 Jul 2021 - 18:37

214

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Extension degree must be power of prime

Published on 02 Sep 2021 - 5:00

43

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How to obtain an expression for a complex differential equation

Published on 16 Sep 2021 - 12:15

List Question

For which $p$ is $\mathbb F_p(X)$ separable over $\mathbb F_p(X^6)$?

Theorem 17.22 from Ian Stewart's Galois Theory

Normal closure as the compositum of conjugates

Unseparable element becomes separable

Inseparable field extension of degree 2

How to reduce to the affine case? Number of points in the fibre and the degree of field extension.

Every algebraic extension of a finite field $F$ is separable

Is the proposition $[KL:L]=[K:F]$ iff $K\cap L=F$ for finite Galois extension still hold for separable extension?

Is every isogeny over $\mathbb Q$ separable?

Functional Analysis : A question abaout extensions without use the Banach Theorem or Zorn's lemma .

Equality between degree of separability of field extensions.

Is an algebraic extension of a separably closed field separably closed?

Let $K=F(u)$ be a separable extension of $F$ with $u^m\in F$. Show that if the characteristic of $F$ is $p$ and $m=p^tr$, then $u^r\in F$.

Extension degree must be power of prime

How to obtain an expression for a complex differential equation

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