List questions from extension-field

Published on 11 Jun 2019 - 20:40

269

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An exercise from Rotman's advanced modern algebra

Published on 14 Jun 2019 - 15:20

54

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$E/F$ finite and separable, $\alpha \in E$, then the irreducible polynomial of $\alpha$ over $F$ is separable. With Lang's definition.

Published on 23 Feb 2026 - 3:01

387

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Extension of a field homomorphism $K(\alpha) \to \overline{K}$ to normal extension $L/K$

Published on 16 Jun 2019 - 19:55

208

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Restriction of element in Galois Group

Published on 17 Jun 2019 - 13:19

179

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Prove that this extension is algebraic

Published on 20 Jun 2019 - 4:14

222

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Finding $[\mathbb{Q}(\sqrt{3}, i\sqrt{2}):\mathbb{Q}(\sqrt{3})]$

Published on 22 Jun 2019 - 8:51

30

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Does the $\mathrm{Spec}(F)$ equal $\overline{F}$ for a field $F$?

Published on 22 Jun 2019 - 18:20

193

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Minimal polynomial of an element of the field extension $L/ \mathbb{F}_2$.

Published on 24 Jun 2019 - 18:57

172

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About ramification groups

Published on 25 Mar 2026 - 7:38

49

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Why $k[X]/\langle f\rangle$ is a field?

Published on 27 Jun 2019 - 4:11

222

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For $\alpha = \sqrt[3]{2} + i$, find the minimal polynomial over $\mathbb{Q}$ and over $\mathbb{Q}[\sqrt[3]{2}]$

Published on 27 Mar 2026 - 5:39

624

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Solvable Field Extension

Published on 25 Mar 2026 - 7:38

260

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Galois is conserved under completions

Published on 27 Mar 2026 - 6:59

336

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Compositum $FL/F$ Galois if $L/K$ Galois

Published on 29 Jun 2019 - 17:52

List Question

Prove that $\exists$ a subfield of a particular degree

An exercise from Rotman's advanced modern algebra

$E/F$ finite and separable, $\alpha \in E$, then the irreducible polynomial of $\alpha$ over $F$ is separable. With Lang's definition.

Extension of a field homomorphism $K(\alpha) \to \overline{K}$ to normal extension $L/K$

Restriction of element in Galois Group

Prove that this extension is algebraic

Finding $[\mathbb{Q}(\sqrt{3}, i\sqrt{2}):\mathbb{Q}(\sqrt{3})]$

Does the $\mathrm{Spec}(F)$ equal $\overline{F}$ for a field $F$?

Minimal polynomial of an element of the field extension $L/ \mathbb{F}_2$.

About ramification groups

Why $k[X]/\langle f\rangle$ is a field?

For $\alpha = \sqrt[3]{2} + i$, find the minimal polynomial over $\mathbb{Q}$ and over $\mathbb{Q}[\sqrt[3]{2}]$

Solvable Field Extension

Galois is conserved under completions

Compositum $FL/F$ Galois if $L/K$ Galois

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