List questions from splitting-field

Published on 01 Jan 2019 - 17:41

40

Views

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 05 Jan 2019 - 20:29

550

Views

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

Published on 08 Jan 2019 - 13:35

122

Views

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

Published on 09 Jan 2019 - 8:42

40

Views

Degree of splitting fields

Published on 09 Jan 2019 - 10:10

50

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

Published on 16 Jan 2019 - 9:55

238

Views

Complex conjugate and Field Extension

Published on 16 Jan 2019 - 13:00

41

Views

Separable polynomial and characteristic of field

Published on 18 Jan 2019 - 4:18

328

Views

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

Published on 25 Jan 2019 - 1:16

160

Views

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

Published on 29 Jan 2019 - 16:06

943

Views

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

Published on 29 Jan 2019 - 22:49

73

Views

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

Published on 30 Jan 2019 - 16:42

42

Views

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

Published on 03 Feb 2019 - 15:29

85

Views

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

Published on 08 Feb 2019 - 5:32

77

Views

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 22 Mar 2026 - 21:22

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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