List questions from splitting-field

Published on 12 Apr 2026 - 21:50

43

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Prove that if $p \not\equiv 1 \hspace{0.2 cm} (5)$ then $f(x) = x^{5} - 2$ has a unique solution in $\mathbb{F}_{p}$

Published on 16 Apr 2026 - 20:51

553

Views

Are radical extensions splitting fields?-Confusion (need help)

Published on 11 Apr 2026 - 19:20

125

Views

Finding the degree of $\mathbb{Q}(\sqrt{3+\sqrt{7}},\sqrt{3-\sqrt{7}})/\mathbb{Q}(\sqrt{3+\sqrt{7}})$

Published on 16 Apr 2026 - 18:05

44

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Degree of splitting fields

Published on 11 May 2026 - 0:10

53

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Splitting Field of a Polynomial in $\mathbb{Q}$

Published on 13 Apr 2026 - 1:50

241

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Complex conjugate and Field Extension

Published on 13 Apr 2026 - 10:48

44

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Separable polynomial and characteristic of field

Published on 13 Apr 2026 - 2:44

331

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Prove that $[\mathbb{Q}(\sqrt{4+\sqrt{5}},\sqrt{4-\sqrt{5}}):\mathbb{Q}] = 8$.

Published on 17 Apr 2026 - 9:49

163

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Splitting field of an irreductible polynomial $f(X) \in F_{q}[X]$

Published on 15 Apr 2026 - 6:26

946

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Prove that $[ \mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}]=8.$

Published on 17 Apr 2026 - 16:02

76

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The degree of a splitting field over $\mathbb{F}_p$ of non-reducible monic polynomial of degree $n$

Published on 14 Apr 2026 - 0:21

44

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Splitting field of $f=t^{4}+2\in \mathbb{Z}_{3}[t]$

Published on 15 Apr 2026 - 21:54

88

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Find the splitting field $K$ of $x^{12}-9$ over $\mathbb{Q}$ and determine $[K:\mathbb{Q}]$.

Published on 16 Apr 2026 - 4:40

83

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Determine $[\mathbb{Q}(\sqrt[4]{11}+i\sqrt[4]{11}):\mathbb{Q}]$, and determine if $\mathbb{Q}(\sqrt[4]{11}+i\sqrt[4]{11})/\mathbb{Q}$ is normal

Published on 10 May 2026 - 20:35

List Question

Minimal polynomial for normal closure

Prove that if $p \not\equiv 1 \hspace{0.2 cm} (5)$ then $f(x) = x^{5} - 2$ has a unique solution in $\mathbb{F}_{p}$

Are radical extensions splitting fields?-Confusion (need help)

Finding the degree of $\mathbb{Q}(\sqrt{3+\sqrt{7}},\sqrt{3-\sqrt{7}})/\mathbb{Q}(\sqrt{3+\sqrt{7}})$

Degree of splitting fields

Splitting Field of a Polynomial in $\mathbb{Q}$

Complex conjugate and Field Extension

Separable polynomial and characteristic of field

Prove that $[\mathbb{Q}(\sqrt{4+\sqrt{5}},\sqrt{4-\sqrt{5}}):\mathbb{Q}] = 8$.

Splitting field of an irreductible polynomial $f(X) \in F_{q}[X]$

Prove that $[ \mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}]=8.$

The degree of a splitting field over $\mathbb{F}_p$ of non-reducible monic polynomial of degree $n$

Splitting field of $f=t^{4}+2\in \mathbb{Z}_{3}[t]$

Find the splitting field $K$ of $x^{12}-9$ over $\mathbb{Q}$ and determine $[K:\mathbb{Q}]$.

Determine $[\mathbb{Q}(\sqrt[4]{11}+i\sqrt[4]{11}):\mathbb{Q}]$, and determine if $\mathbb{Q}(\sqrt[4]{11}+i\sqrt[4]{11})/\mathbb{Q}$ is normal

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