List questions from splitting-field

Published on 10 May 2026 - 16:05

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Splitting field of $f(x) :=x^3+3x^2+3x-4$ over $\Bbb{Q}$ and $\Bbb{Z}_3$.

Published on 16 Apr 2026 - 3:28

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Splitting Field, irreducibility and degree n!

Published on 12 Apr 2026 - 7:25

74

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About Spliting Field

Published on 14 Apr 2026 - 23:32

49

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Check whether the polynomial is irreducible or not

Published on 15 Apr 2026 - 15:54

46

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Can two splitting fields over the same field of a polynomial be different (in the set sense and not up to isomorphism)?

Published on 12 Apr 2026 - 21:26

116

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degree of splitting field of p(q(x))

Published on 15 Apr 2026 - 3:28

105

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degree of splitting field of palindromic polynomial

Published on 09 Apr 2026 - 6:41

78

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Show that $R$ is a field.

Published on 30 Apr 2026 - 14:31

138

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Find the condition on $a, b$ such that the field of $x^3+ax+b\in\Bbb{Q}[x]$ has degree of extension 6.

Published on 16 Apr 2026 - 1:19

54

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Showing that the splitting fields of $x^{2^m}+1$ and $x^{2^{m+1}}-1$ over $\mathbb{F}_p$ are isomorphic.

Published on 16 Apr 2026 - 11:38

538

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Splitting field extension of degree $n!$

Published on 11 Apr 2026 - 9:41

71

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How to determine splitting field on $\mathbb{Q}$ of $f(X)= x^{15}-x^8-x^7+1$ and determine the degree over $\mathbb{Q}$

Published on 16 Apr 2026 - 12:48

572

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Find the smallest normal extension (upto isomorphism) of $\Bbb{Q}(2^{1/4}, 3^{1/4})$ in $\overline{\Bbb{Q}}.$

Published on 16 Apr 2026 - 19:04

260

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Finding the splitting field of $x^4+x^2-6$ over $\mathbb{Z_7}$ and $\mathbb{Z_{13}}$

Published on 16 Apr 2026 - 16:29

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Question on splitting fields.

Splitting field of $f(x) :=x^3+3x^2+3x-4$ over $\Bbb{Q}$ and $\Bbb{Z}_3$.

Splitting Field, irreducibility and degree n!

About Spliting Field

Check whether the polynomial is irreducible or not

Can two splitting fields over the same field of a polynomial be different (in the set sense and not up to isomorphism)?

degree of splitting field of p(q(x))

degree of splitting field of palindromic polynomial

Show that $R$ is a field.

Find the condition on $a, b$ such that the field of $x^3+ax+b\in\Bbb{Q}[x]$ has degree of extension 6.

Showing that the splitting fields of $x^{2^m}+1$ and $x^{2^{m+1}}-1$ over $\mathbb{F}_p$ are isomorphic.

Splitting field extension of degree $n!$

How to determine splitting field on $\mathbb{Q}$ of $f(X)= x^{15}-x^8-x^7+1$ and determine the degree over $\mathbb{Q}$

Find the smallest normal extension (upto isomorphism) of $\Bbb{Q}(2^{1/4}, 3^{1/4})$ in $\overline{\Bbb{Q}}.$

Finding the splitting field of $x^4+x^2-6$ over $\mathbb{Z_7}$ and $\mathbb{Z_{13}}$

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