List questions from extension-field

Published on 14 May 2019 - 21:09

216

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Map induced on fraction fields is finite

Published on 15 May 2019 - 11:47

76

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Is there a general formula for $\left [ \mathbb{Q}(a,b):\mathbb{Q}(a) \right ]$?

Published on 15 May 2019 - 20:55

86

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Intermediate field and Galois extension.

Published on 28 Mar 2026 - 1:02

108

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Prove that $\mathbb{Q}(\zeta_{2^{n+2}} + (\zeta_{2^{n+2}})^{-1})$ is a cyclic field extension of $\mathbb{Q}$ of degree $2^n$.

Published on 16 May 2019 - 16:45

135

Views

Find the irreducible polynomial over $Q$(linear combination of primitive cubic roots)

Published on 26 Mar 2026 - 14:34

150

Views

Showing that $\sqrt{5} \in \mathbb{Q}(\sqrt[p]{2} + \sqrt{5})$

Published on 19 May 2019 - 15:21

50

Views

Zeros in Splitting Factor Rings

Published on 25 Mar 2026 - 12:22

1.8k

Views

Prove every finite extension is a simple extension

Published on 21 May 2019 - 1:41

138

Views

Finitely generated extension implies finitely generated field?

Published on 21 May 2019 - 14:10

47

Views

Relation between $[L \cap M : K \cap M]$ and $[L : K]$, and the Wantzel theorem

Published on 26 Mar 2026 - 3:00

84

Views

Equivalence relation on field extensions, explanation

Published on 29 Mar 2026 - 13:40

1.3k

Views

Proof of finite subfields for a finite field extension

Published on 25 May 2019 - 15:32

110

Views

$p$'th roots in an extension of prime degree $p$.

Published on 28 Mar 2026 - 6:40

95

Views

$\mathbf{Q}[2^{1/3}w]$ = $\mathbf{Q}[2^{1/3},w]$?

Published on 28 May 2019 - 12:12

List Question

Find the Galois group of $\mathbb{Q}(\sqrt{4+\sqrt{7}})/\mathbb{Q}$

Map induced on fraction fields is finite

Is there a general formula for $\left [ \mathbb{Q}(a,b):\mathbb{Q}(a) \right ]$?

Intermediate field and Galois extension.

Prove that $\mathbb{Q}(\zeta_{2^{n+2}} + (\zeta_{2^{n+2}})^{-1})$ is a cyclic field extension of $\mathbb{Q}$ of degree $2^n$.

Find the irreducible polynomial over $Q$(linear combination of primitive cubic roots)

Showing that $\sqrt{5} \in \mathbb{Q}(\sqrt[p]{2} + \sqrt{5})$

Zeros in Splitting Factor Rings

Prove every finite extension is a simple extension

Finitely generated extension implies finitely generated field?

Relation between $[L \cap M : K \cap M]$ and $[L : K]$, and the Wantzel theorem

Equivalence relation on field extensions, explanation

Proof of finite subfields for a finite field extension

$p$'th roots in an extension of prime degree $p$.

$\mathbf{Q}[2^{1/3}w]$ = $\mathbf{Q}[2^{1/3},w]$?

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