List questions from galois-extensions

Published on 15 Apr 2026 - 15:52

120

Views

Skew fields with nonzero characteristic

Published on 09 Apr 2026 - 15:19

49

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Is true that the number of elements in Gal$(F(u)/F)$ is equal the number of distincts roots of its minimal polynomial on $F(u)$?

Published on 15 Apr 2026 - 11:42

64

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What is the Galois group of this extension?

Published on 11 Apr 2026 - 8:16

88

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About the primitive elements of $\mathbb{Q}(\sqrt{3},i\sqrt{5})$

Published on 16 Apr 2026 - 12:05

146

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Countability of Gal(C/Q) and isomorphism of its subgroups

Published on 11 Apr 2026 - 0:54

71

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Galois: Why does $\{1,f,f^2\}$ correspond to $\mathbb{Q}(\omega)$?

Published on 14 Apr 2026 - 18:15

84

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Galois Correspondence as it relates to $\mathbb{Q}(\sqrt{1 + \sqrt{2}})$

Published on 16 Apr 2026 - 11:03

77

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Galois Action on Absolutely Irreducible Polynomials

Published on 13 Apr 2026 - 14:58

61

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Prove that if $N, M \leq\operatorname{Aut}(K/F) $ in a galois extension $K/F $, the fixed field of $\langle N, M \rangle $ is $F^N \cap F^M $

Published on 10 May 2026 - 23:31

49

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Intersection of fixed fields

Published on 13 Apr 2026 - 18:14

73

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The automorphism group of $E(\alpha)/F(\alpha)$

Published on 12 Apr 2026 - 23:29

150

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Galois group of $x^4-11$

Published on 14 Apr 2026 - 5:38

182

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How to see that the cyclotomic extension is a separable extension?

Published on 13 Apr 2026 - 12:49

52

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$K := \mathbb{Q}( \sqrt{5}, \sqrt{−1})$ is a Galois extension of $\mathbb{Q}$ of degree 4

Published on 18 Apr 2026 - 12:54

List Question

Simple argument that field automorphisms can extend

Skew fields with nonzero characteristic

Is true that the number of elements in Gal$(F(u)/F)$ is equal the number of distincts roots of its minimal polynomial on $F(u)$?

What is the Galois group of this extension?

About the primitive elements of $\mathbb{Q}(\sqrt{3},i\sqrt{5})$

Countability of Gal(C/Q) and isomorphism of its subgroups

Galois: Why does $\{1,f,f^2\}$ correspond to $\mathbb{Q}(\omega)$?

Galois Correspondence as it relates to $\mathbb{Q}(\sqrt{1 + \sqrt{2}})$

Galois Action on Absolutely Irreducible Polynomials

Prove that if $N, M \leq\operatorname{Aut}(K/F) $ in a galois extension $K/F $, the fixed field of $\langle N, M \rangle $ is $F^N \cap F^M $

Intersection of fixed fields

The automorphism group of $E(\alpha)/F(\alpha)$

Galois group of $x^4-11$

How to see that the cyclotomic extension is a separable extension?

$K := \mathbb{Q}( \sqrt{5}, \sqrt{−1})$ is a Galois extension of $\mathbb{Q}$ of degree 4

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