List questions from extension-field

Published on 14 Apr 2026 - 2:59

947

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constructing a Galois group for a cyclotomic extension of $\mathbb{Q}$

Published on 14 Apr 2026 - 23:28

7.1k

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Why is the Galois group for a cyclotomic extension isomorphic to $Z_n^{\times}$ and not to $Z_{n-1}$?

Published on 14 Apr 2026 - 3:21

164

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Prove that $ \sigma(x) $ and $ x $ are conjugate over $ F $

Published on 17 Apr 2026 - 7:45

355

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Give all extensions of the mapping to an isomorphic mapping

Published on 16 Apr 2026 - 15:19

250

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Show that Gal$(E/\mathbb{Q})$ is abelian, where $E$ is the splitting field of $f(x)=x^{14} - 1$

Published on 14 Apr 2026 - 22:26

435

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About some properties of composites of field extesions

Published on 10 Apr 2026 - 16:17

1.9k

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The degree of the field extension $\mathbb{Q}(\sqrt{5},w): \mathbb{Q}$

Published on 16 Apr 2026 - 3:35

92

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Extension of field homomorphisms and pullback square

Published on 14 Apr 2026 - 16:54

379

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All intermediate sub extensions of $\mathbb{Q} \subseteq K \subseteq \mathbb{Q}(\zeta_8)$.

Published on 17 Apr 2026 - 2:30

96

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Prove that $F \subset \sigma L$ is also radical.

Published on 16 Apr 2026 - 7:34

47

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Some natural question on subfield of Galois extension

Published on 12 Apr 2026 - 6:19

168

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Field extension equality using Kronecker theorem

Published on 09 Apr 2026 - 18:39

205

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Minimal polynomial of a primitive element for Galois extensions with Galois group $S_n$

Published on 11 Apr 2026 - 23:37

1.6k

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Subfield of $\mathbb{Q}(\sqrt[n]{a})$

Published on 16 Apr 2026 - 4:29

List Question

Showing that a field $k$ is a splitting field for $p(x) \in \mathbb{Q}$

constructing a Galois group for a cyclotomic extension of $\mathbb{Q}$

Why is the Galois group for a cyclotomic extension isomorphic to $Z_n^{\times}$ and not to $Z_{n-1}$?

Prove that $ \sigma(x) $ and $ x $ are conjugate over $ F $

Give all extensions of the mapping to an isomorphic mapping

Show that Gal$(E/\mathbb{Q})$ is abelian, where $E$ is the splitting field of $f(x)=x^{14} - 1$

About some properties of composites of field extesions

The degree of the field extension $\mathbb{Q}(\sqrt{5},w): \mathbb{Q}$

Extension of field homomorphisms and pullback square

All intermediate sub extensions of $\mathbb{Q} \subseteq K \subseteq \mathbb{Q}(\zeta_8)$.

Prove that $F \subset \sigma L$ is also radical.

Some natural question on subfield of Galois extension

Field extension equality using Kronecker theorem

Minimal polynomial of a primitive element for Galois extensions with Galois group $S_n$

Subfield of $\mathbb{Q}(\sqrt[n]{a})$

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