List questions from extension-field

Published on 22 Mar 2026 - 5:45

359

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The number of isomorphisms $\psi$ extending $\phi$ is less than or equal to $[E:F]$

Published on 22 Mar 2026 - 11:00

105

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$\mathbb{Q}(\theta) \neq \mathbb{Q}(\sqrt[3]{d})$.

Published on 02 Feb 2018 - 1:50

244

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Is $\sqrt[6]{3} \in \mathbb{Q}(\sqrt[8]{21})$ and/or $\sqrt[4]{5} \in \mathbb{Q}(e^{\frac{2 \pi i}{25}})$?

Published on 20 Mar 2026 - 3:58

121

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Preserving transcendence degree

Published on 22 Mar 2026 - 0:47

133

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A curious extension of real number field?

Published on 04 Feb 2018 - 22:54

123

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Preservation of $\exists \forall $-sentence of infinite algebraic extension fields

Published on 24 Mar 2026 - 22:08

1.1k

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basis for the splitting field of $x^3 - 3$ over the rationals

Published on 20 Mar 2026 - 9:08

88

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Ruler and compass construction field extension

Published on 23 Mar 2026 - 10:41

1.5k

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Algebraic Field Extension of Finite Field

Published on 06 Feb 2018 - 21:13

259

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

Published on 22 Mar 2026 - 4:24

14.1k

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What is the algebraic closure of $\mathbb{Q}$?

Published on 17 Mar 2026 - 10:46

99

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Existentially closed Field property

Published on 24 Mar 2026 - 23:41

534

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What is the automorphism group $Aut_{\mathbb{Q}} \mathbb{Q}(\sqrt{3}+\sqrt{2})$?

Published on 07 Feb 2018 - 19:04

158

Views

Proving the tower law through an inductive proof

Published on 08 Feb 2018 - 1:52

List Question

Is Homomorphism equivalent to Field extension?

The number of isomorphisms $\psi$ extending $\phi$ is less than or equal to $[E:F]$

$\mathbb{Q}(\theta) \neq \mathbb{Q}(\sqrt[3]{d})$.

Is $\sqrt[6]{3} \in \mathbb{Q}(\sqrt[8]{21})$ and/or $\sqrt[4]{5} \in \mathbb{Q}(e^{\frac{2 \pi i}{25}})$?

Preserving transcendence degree

A curious extension of real number field?

Preservation of $\exists \forall $-sentence of infinite algebraic extension fields

basis for the splitting field of $x^3 - 3$ over the rationals

Ruler and compass construction field extension

Algebraic Field Extension of Finite Field

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

What is the algebraic closure of $\mathbb{Q}$?

Existentially closed Field property

What is the automorphism group $Aut_{\mathbb{Q}} \mathbb{Q}(\sqrt{3}+\sqrt{2})$?

Proving the tower law through an inductive proof

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