Question

Set-theoretic equality of splitting fields within a fixed algebraic closure

score 174 · Answer 1 · 2026-03-21 21:35:29

174

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Set-theoretic equality of splitting fields within a fixed algebraic closure

Published on 21 Mar 2026 - 21:35

score 93 · Answer 2 · 2026-03-25 02:56:36

93

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About splitting fields and primitive elements.

Published on 25 Mar 2026 - 2:56

score 593 · Answer 3 · 2026-03-25 03:04:33

593

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Let $ f(x) ∈ F[x] \ $ and $ \ a ∈ F \ $. Show that $ \ f(x) \ $ and $ \ f(x + a) \ $ have the same splitting field over $ \ F $

Published on 25 Mar 2026 - 3:04

score 213 · Answer 4 · 2018-02-17 00:27:14

213

Views

Find the splitting field of a polynomial over $Z_{p}$

Published on 17 Feb 2018 - 0:27

score 67 · Answer 5 · 2026-03-25 06:05:10

67

Views

On the splitting field over $\mathbb{Q}$ of $X^4 + 1$.

Published on 25 Mar 2026 - 6:05

score 132 · Answer 6 · 2018-03-06 00:07:14

132

Views

On proving that a splitting field over a field $L$ is also a splitting field over a subfield of $L$

Published on 06 Mar 2018 - 0:07

score 124 · Answer 7 · 2018-03-07 04:04:31

124

Views

Splitting field for the polynomial $x^3 + 1 \in \mathbb{Z}_2[x]$ is a subfield of the splitting field of $x^5 + 1 \in \mathbb{Z}_2[x]$

Published on 07 Mar 2018 - 4:04

score 985 · Answer 8 · 2026-03-22 06:02:04

985

Views

Galois group of $x^n+1$ over $\Bbb Q$

Published on 22 Mar 2026 - 6:02

score 175 · Answer 9 · 2026-03-22 12:33:14

175

Views

Showing two splitting fields are different

Published on 22 Mar 2026 - 12:33

score 95 · Answer 10 · 2026-03-22 01:01:40

95

Views

Splitting fields isomorphic

Published on 22 Mar 2026 - 1:01

score 70 · Answer 11 · 2026-03-25 03:21:19

70

Views

Let $p(x) = x^3 + x + 1 \in \mathbb Z_2[x]$ and $E = \mathbb Z_2[x]/p(x)$. Factor $p(x)$ into linear factors in $E[x]$.

Published on 25 Mar 2026 - 3:21

score 461 · Answer 12 · 2026-03-25 06:06:59

461

Views

splitting field of $(x^2-3)(x^2-5)$ over $Q(\sqrt{ 2})$. Am I thinking of this correctly?

Published on 25 Mar 2026 - 6:06

score 230 · Answer 13 · 2018-03-22 20:25:30

230

Views

Is $i\sqrt[4]{10} \in \Bbb Q(\sqrt[4]{10})$ or is my proof wrong?

Published on 22 Mar 2018 - 20:25

score 107 · Answer 14 · 2026-03-25 05:59:42

107

Views

How much do you need to prove when finding splitting fields?

Published on 25 Mar 2026 - 5:59

score 64 · Answer 15 · 2018-03-23 12:01:36

64

Views

What is the difference between $\mathbb{Q}(\alpha,i\alpha)$ and $\mathbb{Q}(\alpha,i)$? Where $\alpha = \sqrt[4]{10}$.

Published on 23 Mar 2018 - 12:01

List Question

Set-theoretic equality of splitting fields within a fixed algebraic closure

About splitting fields and primitive elements.

Let $ f(x) ∈ F[x] \ $ and $ \ a ∈ F \ $. Show that $ \ f(x) \ $ and $ \ f(x + a) \ $ have the same splitting field over $ \ F $

Find the splitting field of a polynomial over $Z_{p}$

On the splitting field over $\mathbb{Q}$ of $X^4 + 1$.

On proving that a splitting field over a field $L$ is also a splitting field over a subfield of $L$

Splitting field for the polynomial $x^3 + 1 \in \mathbb{Z}_2[x]$ is a subfield of the splitting field of $x^5 + 1 \in \mathbb{Z}_2[x]$

Galois group of $x^n+1$ over $\Bbb Q$

Showing two splitting fields are different

Splitting fields isomorphic

Let $p(x) = x^3 + x + 1 \in \mathbb Z_2[x]$ and $E = \mathbb Z_2[x]/p(x)$. Factor $p(x)$ into linear factors in $E[x]$.

splitting field of $(x^2-3)(x^2-5)$ over $Q(\sqrt{ 2})$. Am I thinking of this correctly?

Is $i\sqrt[4]{10} \in \Bbb Q(\sqrt[4]{10})$ or is my proof wrong?

How much do you need to prove when finding splitting fields?

What is the difference between $\mathbb{Q}(\alpha,i\alpha)$ and $\mathbb{Q}(\alpha,i)$? Where $\alpha = \sqrt[4]{10}$.

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