Question

Find the degree of splitting field of a separable polynomial over finite field

score 397 · Answer 1 · 2026-02-22 19:53:45

397

Views

Find the degree of splitting field of a separable polynomial over finite field

Published on 22 Feb 2026 - 19:53

score 1.6k · Answer 2 · 2018-01-21 05:37:45

1.6k

Views

If $\alpha$ separable over $F$ then $F(\alpha )/F$ is a separable extension.

Published on 21 Jan 2018 - 5:37

score 921 · Answer 3 · 2018-01-28 12:21:36

921

Views

non separable, non normal, finite field extension

Published on 28 Jan 2018 - 12:21

score 181 · Answer 4 · 2018-02-02 20:53:31

181

Views

Is $\mathbb{F}_q(x)$ a perfect field?

Published on 02 Feb 2018 - 20:53

score 112 · Answer 5 · 2018-02-02 21:44:41

112

Views

Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?

Published on 02 Feb 2018 - 21:44

score 251 · Answer 6 · 2018-02-07 03:10:44

251

Views

Converse to Prop. V.6.11 from Lang's Algebra: $E/k$ normal $\impliedby E^{\operatorname{Aut}(E/k)}/k $ purely inseparable?

Published on 07 Feb 2018 - 3:10

score 71 · Answer 7 · 2018-03-25 14:28:22

71

Views

If $E/k$ is not separable, but satisfies the property that there exists a positive integer $n$ for which every $\alpha \in E$ of degree less than $n$

Published on 25 Mar 2018 - 14:28

score 1.1k · Answer 8 · 2018-04-28 14:24:32

1.1k

Views

Let $L/K$ be a finite separable field extension. How to prove there are finitely many intermediate fields?

Published on 28 Apr 2018 - 14:24

score 79 · Answer 9 · 2018-05-04 02:22:50

79

Views

Prove this field extension is separable

Published on 04 May 2018 - 2:22

score 89 · Answer 10 · 2018-05-10 22:11:02

89

Views

$\mathbb F_p(t) \leq L $ a finite extension

Published on 10 May 2018 - 22:11

score 684 · Answer 11 · 2018-05-12 23:35:02

684

Views

Suppose $K/F $ is finite with $K = F (K^p) $. If a finite set $S $ is linearly independent, prove that so is $S^p $.

Published on 12 May 2018 - 23:35

score 334 · Answer 12 · 2018-05-13 23:29:31

334

Views

if the tensor product of a finite field extension and the separable closure over base field is a field, then their intersection is the base field

Published on 13 May 2018 - 23:29

score 58 · Answer 13 · 2018-05-16 05:56:13

58

Views

Question about separable polynomial - proof verification

Published on 16 May 2018 - 5:56

score 144 · Answer 14 · 2018-05-17 03:14:22

144

Views

Let $F $ be a field with char $F =p >0$. If $\alpha \in K/F$ is separable over $F $, prove that $F (\alpha)/F $ is separable.

Published on 17 May 2018 - 3:14

score 899 · Answer 15 · 2018-05-17 20:10:57

899

Views

Proving that the polynomial $f(x)$ is separable

Published on 17 May 2018 - 20:10

List Question

Find the degree of splitting field of a separable polynomial over finite field

If $\alpha$ separable over $F$ then $F(\alpha )/F$ is a separable extension.

non separable, non normal, finite field extension

Is $\mathbb{F}_q(x)$ a perfect field?

Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?

Converse to Prop. V.6.11 from Lang's Algebra: $E/k$ normal $\impliedby E^{\operatorname{Aut}(E/k)}/k $ purely inseparable?

If $E/k$ is not separable, but satisfies the property that there exists a positive integer $n$ for which every $\alpha \in E$ of degree less than $n$

Let $L/K$ be a finite separable field extension. How to prove there are finitely many intermediate fields?

Prove this field extension is separable

$\mathbb F_p(t) \leq L $ a finite extension

Suppose $K/F $ is finite with $K = F (K^p) $. If a finite set $S $ is linearly independent, prove that so is $S^p $.

if the tensor product of a finite field extension and the separable closure over base field is a field, then their intersection is the base field

Question about separable polynomial - proof verification

Let $F $ be a field with char $F =p >0$. If $\alpha \in K/F$ is separable over $F $, prove that $F (\alpha)/F $ is separable.

Proving that the polynomial $f(x)$ is separable

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