List questions from normal-extension

Published on 22 Feb 2026 - 21:49

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non separable, non normal, finite field extension

Published on 22 Feb 2026 - 21:47

120

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smallest normal extension containing an infinite algebraic extension

Published on 22 Feb 2026 - 21:48

252

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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 Feb 2026 - 21:52

51

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Intermediate Fields and Root Fields

Published on 22 Feb 2026 - 21:43

185

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Are normal extensions always simple?

Published on 22 Feb 2026 - 21:43

656

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If $L/K$ normal and $H = \operatorname{Aut}(L/K)$, then $L/L^H$ is separable and $L^H/K$ is purely inseparable.

Published on 22 Feb 2026 - 21:53

1.6k

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Finding whether an extension is normal

Published on 22 Feb 2026 - 23:38

145

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What automorphism cannot be extended when the extension is not normal?

Published on 22 Feb 2026 - 21:48

69

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Determine $[\mathbb{Q}(\sqrt[4]{11}+i\sqrt[4]{11}):\mathbb{Q}]$, and determine if $\mathbb{Q}(\sqrt[4]{11}+i\sqrt[4]{11})/\mathbb{Q}$ is normal

Published on 22 Feb 2026 - 21:51

301

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Doubt in Lang's proof that normal extensions remain normal under lifting (Theorem V.3.4, Algebra)

Published on 22 Feb 2026 - 23:08

107

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Help understanding how to show a field extension is a Galois extension .

Published on 22 Feb 2026 - 23:10

198

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Prove if two normal extensions over a field are isomorphic

Published on 22 Feb 2026 - 23:07

248

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Normal Closure of an Algebraic Extension

Published on 22 Feb 2026 - 23:08

878

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Show that an extension $K/F$ with $|K:F| = 2$ is normal.

Published on 22 Feb 2026 - 23:10

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Property of Splitting Fields and K-homomorphisms

non separable, non normal, finite field extension

smallest normal extension containing an infinite algebraic extension

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

Intermediate Fields and Root Fields

Are normal extensions always simple?

If $L/K$ normal and $H = \operatorname{Aut}(L/K)$, then $L/L^H$ is separable and $L^H/K$ is purely inseparable.

Finding whether an extension is normal

What automorphism cannot be extended when the extension is not normal?

Determine $[\mathbb{Q}(\sqrt[4]{11}+i\sqrt[4]{11}):\mathbb{Q}]$, and determine if $\mathbb{Q}(\sqrt[4]{11}+i\sqrt[4]{11})/\mathbb{Q}$ is normal

Doubt in Lang's proof that normal extensions remain normal under lifting (Theorem V.3.4, Algebra)

Help understanding how to show a field extension is a Galois extension .

Prove if two normal extensions over a field are isomorphic

Normal Closure of an Algebraic Extension

Show that an extension $K/F$ with $|K:F| = 2$ is normal.

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