List questions from galois-theory

Published on 28 Mar 2026 - 6:01

63

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Factoring Polynomials into Galois Conjugate Linear Factors

Published on 29 Mar 2026 - 14:19

236

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Check that the corresponding extensions are normal

Published on 28 Mar 2026 - 1:02

75

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Is the extension $\mathbb{Q}(\alpha)/\mathbb{Q}$, where $\alpha = 2\pi i /3$, a splitting extension?

Published on 31 Mar 2026 - 18:37

35

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L:K algebraic and separable then [L:K] $\leq$ n

Published on 14 May 2019 - 10:24

109

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Prove: Permutation of a root is another root of a polynomial

Published on 14 May 2019 - 12:35

371

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

Published on 31 Mar 2026 - 20:30

69

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A question about Galois extension and splitting field of an irreducible polynomial

Published on 28 Mar 2026 - 1:02

77

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

Published on 31 Mar 2026 - 20:24

86

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Intermediate field and Galois extension.

Published on 28 Mar 2026 - 1:02

804

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Show that the Galois extension is isomorphic to $\mathbb{Z}_2\times \mathbb{Z}_2$

Published on 28 Mar 2026 - 2:42

109

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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 31 Mar 2026 - 20:28

463

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Problem on cyclotomic field

Published on 31 Mar 2026 - 21:56

47

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Show that the Galois extension $\cong H\rtimes \mathbb{Z}_2$

Published on 28 Mar 2026 - 2:43

334

Views

Kummer Generators for Cyclic Extensions

Published on 22 Mar 2026 - 8:52

List Question

Quartic as a product of quadratics

Factoring Polynomials into Galois Conjugate Linear Factors

Check that the corresponding extensions are normal

Is the extension $\mathbb{Q}(\alpha)/\mathbb{Q}$, where $\alpha = 2\pi i /3$, a splitting extension?

L:K algebraic and separable then [L:K] $\leq$ n

Prove: Permutation of a root is another root of a polynomial

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

A question about Galois extension and splitting field of an irreducible polynomial

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

Intermediate field and Galois extension.

Show that the Galois extension is isomorphic to $\mathbb{Z}_2\times \mathbb{Z}_2$

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

Problem on cyclotomic field

Show that the Galois extension $\cong H\rtimes \mathbb{Z}_2$

Kummer Generators for Cyclic Extensions

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