List questions from galois-theory

64

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Splitting field's Galois group of $p(X)=X^4+(t^3+1)$ over $\mathbb{Q}(t)$ where $t$ transcendent over $\mathbb{Q}$

Published on 28 Mar 2026 - 11:21

505

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When does adjoining a single root of an irreducible polynomial generate the splitting field?

Published on 04 Apr 2026 - 3:54

83

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Is $\Bbb Q（sin2π/n）$ is Galois over $\Bbb Q$?

Published on 30 Jan 2020 - 10:30

157

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Marcus Number Fields exercise 31 chapter 5

Published on 30 Jan 2020 - 15:21

235

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Inverse limit of Galois groups of a finite Galois extension $K/F$

Published on 01 Apr 2026 - 15:43

553

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Proof verification -- $x^p - x + a$ is irreducible over a field of characteristic $p$

Published on 28 Mar 2026 - 11:13

143

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Question about Galois group (acts transitively on roots)

Published on 31 Jan 2020 - 19:55

117

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Can $\mathbb{Q}(u)$ be of degree 2 over $\mathbb{Q} (u^3)$?

Published on 26 Mar 2026 - 14:30

70

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Calculate the fixed field of these automorphisms

Published on 29 Mar 2026 - 8:44

59

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Reference request: some properties of Dedekind rings

Published on 25 Mar 2026 - 17:36

82

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Properties of Finite Galois Extensions

Published on 05 Feb 2020 - 17:12

173

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Show Gal(f) is cyclic

Published on 26 Mar 2026 - 14:28

81

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Existence of finite Galois extensions

Published on 06 Feb 2020 - 1:25

91

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Splitting field of $\alpha=(2+\sqrt{2})^{1/3}$

Published on 06 Feb 2020 - 18:42

65

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Galois theory: infinite field case

Published on 07 Feb 2020 - 3:25

List Question

Splitting field's Galois group of $p(X)=X^4+(t^3+1)$ over $\mathbb{Q}(t)$ where $t$ transcendent over $\mathbb{Q}$

When does adjoining a single root of an irreducible polynomial generate the splitting field?

Is $\Bbb Q（sin2π/n）$ is Galois over $\Bbb Q$?

Marcus Number Fields exercise 31 chapter 5

Inverse limit of Galois groups of a finite Galois extension $K/F$

Proof verification -- $x^p - x + a$ is irreducible over a field of characteristic $p$

Question about Galois group (acts transitively on roots)

Can $\mathbb{Q}(u)$ be of degree 2 over $\mathbb{Q} (u^3)$?

Calculate the fixed field of these automorphisms

Reference request: some properties of Dedekind rings

Properties of Finite Galois Extensions

Show Gal(f) is cyclic

Existence of finite Galois extensions

Splitting field of $\alpha=(2+\sqrt{2})^{1/3}$

Galois theory: infinite field case

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