List questions from splitting-field

Published on 19 May 2017 - 11:04

309

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How to determine whether an extension is normal extension.

Published on 23 Feb 2026 - 2:46

353

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K-morphism vs K-homomorphism

Published on 26 Mar 2026 - 18:49

120

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Different Representations of GF(8)

Published on 22 May 2017 - 2:06

765

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Prove that if $F$ is a splitting Field of $S$ over $K$ and $E$ is an intermediate field then $F$ is a splitting field of $S$ over $E$.

Published on 23 May 2017 - 3:41

68

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Examples of over $\Bbb Q(i)$ such that the Galois group is (i)$\Bbb Z_2\times \Bbb Z_2$ (ii) $D_4$

Published on 24 May 2017 - 2:47

2k

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Field Extension with Galois group $S_n$ is the splitting field of a polynomial of degree $n$

Published on 25 May 2017 - 22:30

39

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Non-existence of an element in a splitting field -- obvious, but hard to prove

Published on 26 May 2017 - 5:03

199

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Identifying the splitting field of $x^{4}-2x^{2}-3$

Published on 28 May 2017 - 15:55

96

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Can $\sqrt{3}$ be written as a polynomial expression in $\sqrt[3]{3}$ and $\zeta_3$

Published on 29 May 2017 - 7:46

638

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Prove the Galois group of the splitting field of $x^4-4x+2$ is $S_4$

Published on 30 May 2017 - 3:59

1.2k

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Prove $f(x)=x^8-24 x^6+144 x^4-288 x^2+144$ is irreducible over $\mathbb{Q}$

Published on 30 May 2017 - 15:45

71

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(From Milne) Splitting field over a finite field.

Published on 30 May 2017 - 19:09

65

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Having some queries in the proof of $F[x]/Ker(\phi)\simeq F(a)$

Published on 31 May 2017 - 12:22

733

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Is $x^n-a$ irreducible over $\Bbb Q(\zeta_n)$?

Published on 31 May 2017 - 13:11

List Question

Is $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ a Galois extension of $\mathbb{Q}$

How to determine whether an extension is normal extension.

K-morphism vs K-homomorphism

Different Representations of GF(8)

Prove that if $F$ is a splitting Field of $S$ over $K$ and $E$ is an intermediate field then $F$ is a splitting field of $S$ over $E$.

Examples of over $\Bbb Q(i)$ such that the Galois group is (i)$\Bbb Z_2\times \Bbb Z_2$ (ii) $D_4$

Field Extension with Galois group $S_n$ is the splitting field of a polynomial of degree $n$

Non-existence of an element in a splitting field -- obvious, but hard to prove

Identifying the splitting field of $x^{4}-2x^{2}-3$

Can $\sqrt{3}$ be written as a polynomial expression in $\sqrt[3]{3}$ and $\zeta_3$

Prove the Galois group of the splitting field of $x^4-4x+2$ is $S_4$

Prove $f(x)=x^8-24 x^6+144 x^4-288 x^2+144$ is irreducible over $\mathbb{Q}$

(From Milne) Splitting field over a finite field.

Having some queries in the proof of $F[x]/Ker(\phi)\simeq F(a)$

Is $x^n-a$ irreducible over $\Bbb Q(\zeta_n)$?

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