List questions from splitting-field

Published on 12 May 2015 - 6:20

165

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Exercise: splitting field, showing that it splits

Published on 15 May 2015 - 16:34

1.2k

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Find the Galois group of the polynomial $x^{4} + x - 1$ over the finite field $\mathbb{F}_{3}$

Published on 25 May 2015 - 21:19

1.7k

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Show that $\mathbb{F}_q$ is a Splitting Field for Polynomial $x^q-x$

Published on 27 May 2015 - 3:33

5.2k

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Show that $\mathbb{Q}(\sqrt{2 +\sqrt{2}})$ is a cyclic quartic field i.e. is a galois extension of degree 4 with cyclic galois group

Published on 28 May 2015 - 3:09

454

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$\Bbb{Z}_{2}(\alpha)$ as splitting field

Published on 29 May 2015 - 13:43

184

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Is $\mathbb{Q}(\sqrt{2})\subset\mathbb{Q}\left(\sqrt{2},i\sqrt[3]{2}\right)$ a Galois extension?

Published on 08 Jun 2015 - 13:20

441

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Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$

Published on 26 Mar 2026 - 22:54

2.1k

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How should I find Splitting Field of $x^3-2$ over $\mathbb Q$.

Published on 15 Jun 2015 - 11:49

839

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$E/F$ is a normal extension iff $E$ is a splitting field for some polynomial $f\in F[X]$.

Published on 25 Jun 2015 - 13:44

300

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Irreducible polynomial over $\mathbb{Q}(\zeta)$

Published on 28 Jun 2015 - 23:03

723

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Radical extension and algebraic solution of an irreducible polynomial

Published on 06 Jul 2015 - 10:43

1.3k

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Galois Group of $x^{4}+7$

Published on 09 Jul 2015 - 1:04

773

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The Galois group of a specific polynomial $ f(x) = x^6-2x^3+2 \in Q[x] $

Published on 15 Jul 2015 - 11:55

1.7k

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splitting field of $x^8-1$ over $\mathbb F_3$

Published on 17 Jul 2015 - 10:56

List Question

Can it be proved that this extension is algebraic?

Exercise: splitting field, showing that it splits

Find the Galois group of the polynomial $x^{4} + x - 1$ over the finite field $\mathbb{F}_{3}$

Show that $\mathbb{F}_q$ is a Splitting Field for Polynomial $x^q-x$

Show that $\mathbb{Q}(\sqrt{2 +\sqrt{2}})$ is a cyclic quartic field i.e. is a galois extension of degree 4 with cyclic galois group

$\Bbb{Z}_{2}(\alpha)$ as splitting field

Is $\mathbb{Q}(\sqrt{2})\subset\mathbb{Q}\left(\sqrt{2},i\sqrt[3]{2}\right)$ a Galois extension?

Proving that a Galois group $Gal(E/Q)$ is isomorphic to $\mathbb{F}_p^\times$

How should I find Splitting Field of $x^3-2$ over $\mathbb Q$.

$E/F$ is a normal extension iff $E$ is a splitting field for some polynomial $f\in F[X]$.

Irreducible polynomial over $\mathbb{Q}(\zeta)$

Radical extension and algebraic solution of an irreducible polynomial

Galois Group of $x^{4}+7$

The Galois group of a specific polynomial $ f(x) = x^6-2x^3+2 \in Q[x] $

splitting field of $x^8-1$ over $\mathbb F_3$

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