Question

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

score 175 · Answer 1 · 2026-03-25 07:58:46

175

Views

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

Published on 25 Mar 2026 - 7:58

score 95 · Answer 2 · 2026-04-15 15:33:09

95

Views

About splitting fields and primitive elements.

Published on 15 Apr 2026 - 15:33

score 595 · Answer 3 · 2026-04-15 23:47:02

595

Views

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 15 Apr 2026 - 23:47

score 216 · Answer 4 · 2026-04-11 21:41:07

216

Views

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

Published on 11 Apr 2026 - 21:41

score 69 · Answer 5 · 2026-04-16 15:44:17

69

Views

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

Published on 16 Apr 2026 - 15:44

score 135 · Answer 6 · 2026-04-13 23:01:38

135

Views

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

Published on 13 Apr 2026 - 23:01

score 127 · Answer 7 · 2026-04-14 20:12:28

127

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 14 Apr 2026 - 20:12

score 991 · Answer 8 · 2026-04-29 12:41:01

991

Views

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

Published on 29 Apr 2026 - 12:41

score 178 · Answer 9 · 2026-04-09 23:45:42

178

Views

Showing two splitting fields are different

Published on 09 Apr 2026 - 23:45

score 99 · Answer 10 · 2026-04-12 13:02:57

99

Views

Splitting fields isomorphic

Published on 12 Apr 2026 - 13:02

score 72 · Answer 11 · 2026-04-16 07:56:14

72

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 16 Apr 2026 - 7:56

score 463 · Answer 12 · 2026-04-16 10:40:13

463

Views

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

Published on 16 Apr 2026 - 10:40

score 233 · Answer 13 · 2026-04-13 18:18:16

233

Views

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

Published on 13 Apr 2026 - 18:18

score 109 · Answer 14 · 2026-04-10 20:52:46

109

Views

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

Published on 10 Apr 2026 - 20:52

score 67 · Answer 15 · 2026-04-14 23:54:32

67

Views

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

Published on 14 Apr 2026 - 23:54

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 $\alpha = \sqrt[4]{10}$.

Trending Questions

Popular # Hahtags

Popular Questions