List questions from galois-extensions

Published on 13 Apr 2026 - 17:09

947

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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 15 Apr 2026 - 17:28

216

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

Published on 14 May 2026 - 11:41

595

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

Published on 15 May 2026 - 2:44

107

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

Published on 16 Apr 2026 - 7:49

34

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

Published on 15 May 2026 - 6:17

43

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

Published on 26 Mar 2026 - 2:54

105

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Why isn't the splitting field always Galois?

Published on 11 Apr 2026 - 21:42

87

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Algebraic numbers with special properties

Published on 15 May 2026 - 9:20

88

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Quaternion division rings in characteristic $0$

Published on 16 Apr 2026 - 4:56

53

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Question on the discriminant of a irreducible polynomial

Published on 12 Apr 2026 - 15:08

47

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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 13 Apr 2026 - 21:19

120

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

Published on 11 Apr 2026 - 20:33

70

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

Published on 15 Apr 2026 - 10:48

327

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What is an Archimedean prime?

Published on 15 May 2026 - 0:17

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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