List questions from galois-extensions

Published on 14 Feb 2017 - 9:55

944

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let $ K\subseteq M \subseteq L$. If the extensions $M \subseteq L$ and $K \subseteq M$ are separable, then $K\subseteq L$ is separable.

Published on 16 Feb 2017 - 21:53

212

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Extension degree of galois closure of $\mathbb{R}(X^4 -\frac{1}{X^4 })$

Published on 27 Feb 2017 - 14:12

591

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Galois Group of $\mathbb{Q}[\sqrt{3}, \sqrt{5}, \sqrt{7}]$

Published on 03 Apr 2017 - 2:12

104

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Conditions on $K(X)/K(X^n)$ being Galois

Published on 29 Jan 2023 - 15:25

30

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The relation between $Gal(Z_2(M)/Z_1(M))$ and $Gal(Z_2/Z_1)$

Published on 29 Jan 2023 - 15:41

43

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Proof about the closed integral $\mathbb{Z}_p[\zeta_p]$

Published on 26 Mar 2026 - 2:54

102

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Why isn't the splitting field always Galois?

Published on 12 Feb 2023 - 6:56

81

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Algebraic numbers with special properties

Published on 25 Feb 2023 - 19:50

85

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Quaternion division rings in characteristic $0$

Published on 08 Mar 2023 - 13:59

51

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Question on the discriminant of a irreducible polynomial

Published on 25 Mar 2026 - 13:55

44

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Suppose $K$ is a field such that every finite Galois extension of $K$ is cyclic. Is there a name for this property?

Published on 16 Mar 2023 - 20:01

118

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Find a Galois extension whose Galois group is $\mathbb{Z}_4 \times \mathbb{Z}_4$

Published on 26 Mar 2026 - 19:11

67

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Show a field extension is normal, then find the Galois group

Published on 27 Mar 2023 - 1:04

326

Views

What is an Archimedean prime?

Published on 26 Mar 2026 - 2:54

List Question

Algebraic integers in quadratic extensions of rationals

let $ K\subseteq M \subseteq L$. If the extensions $M \subseteq L$ and $K \subseteq M$ are separable, then $K\subseteq L$ is separable.

Extension degree of galois closure of $\mathbb{R}(X^4 -\frac{1}{X^4 })$

Galois Group of $\mathbb{Q}[\sqrt{3}, \sqrt{5}, \sqrt{7}]$

Conditions on $K(X)/K(X^n)$ being Galois

The relation between $Gal(Z_2(M)/Z_1(M))$ and $Gal(Z_2/Z_1)$

Proof about the closed integral $\mathbb{Z}_p[\zeta_p]$

Why isn't the splitting field always Galois?

Algebraic numbers with special properties

Quaternion division rings in characteristic $0$

Question on the discriminant of a irreducible polynomial

Suppose $K$ is a field such that every finite Galois extension of $K$ is cyclic. Is there a name for this property?

Find a Galois extension whose Galois group is $\mathbb{Z}_4 \times \mathbb{Z}_4$

Show a field extension is normal, then find the Galois group

What is an Archimedean prime?

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