List questions from splitting-field

Published on 10 Sep 2018 - 23:06

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

Published on 11 Sep 2018 - 21:30

1.1k

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Splitting Field, irreducibility and degree n!

Published on 16 Sep 2018 - 16:19

70

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About Spliting Field

Published on 24 Sep 2018 - 13:09

46

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Check whether the polynomial is irreducible or not

Published on 25 Sep 2018 - 6:26

43

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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 28 Sep 2018 - 13:38

113

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

Published on 03 Oct 2018 - 5:45

103

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degree of splitting field of palindromic polynomial

Published on 03 Oct 2018 - 15:25

74

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Show that $R$ is a field.

Published on 08 Oct 2018 - 5:55

135

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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 10 Oct 2018 - 16:53

51

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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 11 Oct 2018 - 16:33

535

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Splitting field extension of degree $n!$

Published on 20 Oct 2018 - 13:03

68

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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 23 Oct 2018 - 19:51

570

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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 25 Oct 2018 - 12:36

255

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

Published on 27 Oct 2018 - 18:24

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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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