List questions from galois-theory

Published on 06 Mar 2020 - 13:04

446

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composite field

Published on 29 Mar 2026 - 22:12

75

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Question about finite Galois extensions of F and their intersections.

Published on 28 Mar 2026 - 13:02

39

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Is anyone here familiar with differential field theory or differential galois theory?

Published on 27 Mar 2026 - 22:31

222

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Proving that $f = X^3+2$ is irreducible in $\mathbf{F}_{49}[X]$, and is $f$ irreducible over all $\mathbf{F}_{7^n}$ for $n$ even?

Published on 29 Mar 2026 - 22:09

70

Views

Cubic extension adjoining a root of an irreducible cubic polynomial.

Published on 26 Mar 2026 - 19:00

149

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Powers in discriminants and Galois groups

Published on 12 Mar 2020 - 3:11

326

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Szamuely's "Galois groups and fundamental groups" exercise I.7

Published on 25 Mar 2026 - 14:23

67

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Claim: $[K(\alpha_1, \dots \alpha_i): K] \leq n (n-1) \dots (n-i+1)$ for the splitting field of a separable polynomial of degree $n$

Published on 26 Mar 2026 - 14:30

118

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Minimal polynomial of $\sqrt{3+\sqrt[3]{3}}$

Published on 13 Mar 2020 - 15:21

117

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Abelian extensions are ray class fields

Published on 13 Mar 2020 - 16:07

136

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Degree of a field over a fixed subfield

Published on 13 Mar 2020 - 17:50

380

Views

normal basis theorem-proof finite fields

Published on 01 Apr 2026 - 20:22

110

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Is a normal irreducible separable polynomial of degree $p$ over a field of characteristic $p$ necessarily Artin-Schreier

Published on 25 Mar 2026 - 11:54

78

Views

The action of a Galois group on a cyclotomic field.

Published on 25 Mar 2026 - 8:12

List Question

How to use Cayley's theorem to prove the following?

composite field

Question about finite Galois extensions of F and their intersections.

Is anyone here familiar with differential field theory or differential galois theory?

Proving that $f = X^3+2$ is irreducible in $\mathbf{F}_{49}[X]$, and is $f$ irreducible over all $\mathbf{F}_{7^n}$ for $n$ even?

Cubic extension adjoining a root of an irreducible cubic polynomial.

Powers in discriminants and Galois groups

Szamuely's "Galois groups and fundamental groups" exercise I.7

Claim: $[K(\alpha_1, \dots \alpha_i): K] \leq n (n-1) \dots (n-i+1)$ for the splitting field of a separable polynomial of degree $n$

Minimal polynomial of $\sqrt{3+\sqrt[3]{3}}$

Abelian extensions are ray class fields

Degree of a field over a fixed subfield

normal basis theorem-proof finite fields

Is a normal irreducible separable polynomial of degree $p$ over a field of characteristic $p$ necessarily Artin-Schreier

The action of a Galois group on a cyclotomic field.

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