List questions from splitting-field

Published on 21 Oct 2016 - 17:56

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An exercise about field extensions and roots

Published on 27 Oct 2016 - 19:42

3.3k

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Galois group acting transitively on roots

Published on 04 Nov 2016 - 6:27

507

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Is $\mathbb{Q(\sqrt[4]{-7})/\mathbb{Q}}$ a normal extension?

Published on 16 Nov 2016 - 16:55

5k

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Galois group of the irreducible cubic equation $x^3-3x+1$

Published on 17 Nov 2016 - 2:48

74

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$f\in K[X]\subseteq \mathbb{C}[X]$ with degree $p\geq 5$ irreducible is solvable if and only if $N=K[\alpha_i,\alpha_j]$ for every $i,j$

Published on 17 Nov 2016 - 19:47

870

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Splitting field of $x^6-6\in\mathbb{Q}[x]$

Published on 30 Nov 2016 - 21:02

940

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Find the dimension and a basis of the extension field $\mathbb Q(\sqrt{5},i)$ of $\mathbb Q$.

Published on 30 Nov 2016 - 21:33

595

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Splitting field of $x^5+x+1\in\mathbb{Z}_2[x]$

Published on 30 Nov 2016 - 21:47

264

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Show that $K$ is a splitting field of $f(x)$ over $E$.

Published on 30 Nov 2016 - 22:49

410

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Set of elements fixed by Galois group of $E$ over $F$ if $F$ (requesting alternate proof)

Published on 08 Dec 2016 - 17:43

398

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Splitting field notation confusion

Published on 16 Dec 2016 - 19:43

625

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Splitting fields and Conjugate fields of Number Fields

Published on 21 Dec 2016 - 9:00

391

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Prove that a polynomial with integer coefficients splits into linear factors modulo infinite number of primes

Published on 26 Mar 2026 - 1:14

156

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Simple exercise on Galois theory

Published on 25 Dec 2016 - 18:58

List Question

What is the splitting field for an irreducible polynomial?

An exercise about field extensions and roots

Galois group acting transitively on roots

Is $\mathbb{Q(\sqrt[4]{-7})/\mathbb{Q}}$ a normal extension?

Galois group of the irreducible cubic equation $x^3-3x+1$

$f\in K[X]\subseteq \mathbb{C}[X]$ with degree $p\geq 5$ irreducible is solvable if and only if $N=K[\alpha_i,\alpha_j]$ for every $i,j$

Splitting field of $x^6-6\in\mathbb{Q}[x]$

Find the dimension and a basis of the extension field $\mathbb Q(\sqrt{5},i)$ of $\mathbb Q$.

Splitting field of $x^5+x+1\in\mathbb{Z}_2[x]$

Show that $K$ is a splitting field of $f(x)$ over $E$.

Set of elements fixed by Galois group of $E$ over $F$ if $F$ (requesting alternate proof)

Splitting field notation confusion

Splitting fields and Conjugate fields of Number Fields

Prove that a polynomial with integer coefficients splits into linear factors modulo infinite number of primes

Simple exercise on Galois theory

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