List questions from extension-field

Published on 26 Mar 2026 - 9:49

236

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Field extension of a field of Characteristic $p$

Published on 27 Mar 2026 - 12:44

69

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On the existence of tamely ramified extension

Published on 25 Mar 2026 - 14:26

165

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Galois theory and Field extensions

Published on 09 Nov 2019 - 10:49

106

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Showing $K(\sqrt[3]{t}) / K$ is a normal extension.

Published on 23 Feb 2026 - 1:04

68

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How to prove that the vector space endomorphism $T_x : L \to L, \alpha \mapsto \alpha x$ of $L/K$ has a certain form.

Published on 10 Nov 2019 - 19:36

653

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Proof verification: transcendence degree additive in towers

Published on 02 Apr 2026 - 18:20

626

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Degree of extension $\mathbb{Q}(\cos(2\pi/p),\sin(2\pi/p))/\mathbb{Q}(\cos(2\pi/p))$.

Published on 11 Nov 2019 - 15:36

321

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$A$ reduced implies $A\otimes_k K$ reduced, for $k$ perfect.

Published on 11 Nov 2019 - 17:07

184

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$F$ splitting field of $f(x) \in K[X]$, if Gal$(F|K)$ acts transitively on the roots of $f$, $f$ is irreducible

Published on 12 Nov 2019 - 19:27

116

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Size of a field with field extensions is hopefully equal to $p^n-1$

Published on 01 Apr 2026 - 3:45

129

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Intermediate fields of Galois group of $X^4+8T+12$ and minimal polynomials of their generators

Published on 14 Nov 2019 - 0:39

130

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Does multiplying two intermediate fields give a subfield?

Published on 16 Nov 2019 - 20:57

53

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two extension fields with coprime degrees

Published on 18 Nov 2019 - 5:34

1.1k

Views

Composite of Galois extensions is Galois, a particular proof.

Published on 18 Nov 2019 - 15:33

List Question

Finding primitive element of an extension

Field extension of a field of Characteristic $p$

On the existence of tamely ramified extension

Galois theory and Field extensions

Showing $K(\sqrt[3]{t}) / K$ is a normal extension.

How to prove that the vector space endomorphism $T_x : L \to L, \alpha \mapsto \alpha x$ of $L/K$ has a certain form.

Proof verification: transcendence degree additive in towers

Degree of extension $\mathbb{Q}(\cos(2\pi/p),\sin(2\pi/p))/\mathbb{Q}(\cos(2\pi/p))$.

$A$ reduced implies $A\otimes_k K$ reduced, for $k$ perfect.

$F$ splitting field of $f(x) \in K[X]$, if Gal$(F|K)$ acts transitively on the roots of $f$, $f$ is irreducible

Size of a field with field extensions is hopefully equal to $p^n-1$

Intermediate fields of Galois group of $X^4+8T+12$ and minimal polynomials of their generators

Does multiplying two intermediate fields give a subfield?

two extension fields with coprime degrees

Composite of Galois extensions is Galois, a particular proof.

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