Question

Prove or disprove that the rings $R$ and $S$ are isomorphic.

score 185 · Answer 1 · 2021-03-13 10:10:38

185

Views

Prove or disprove that the rings $R$ and $S$ are isomorphic.

Published on 13 Mar 2021 - 10:10

score 62 · Answer 2 · 2026-04-01 18:34:05

62

Views

Galois group of polynomial over $\mathbb{Q}(\sqrt{-3})$

Published on 01 Apr 2026 - 18:34

score 129 · Answer 3 · 2021-03-14 08:06:02

129

Views

Let $f(x) = x^4 + 2x^2 - 6$ and let E be the splitting field of $f(x)$ over $\mathbb{Q}$.

Published on 14 Mar 2021 - 8:06

score 122 · Answer 4 · 2026-03-31 23:51:32

122

Views

Prove that $|\text{Aut}(F(\alpha)/F)| = |\text{Aut}(F(\beta)/F)|$ and the groups $\text{Aut}(F(\alpha)/F)$ and $\text{Aut}(F(\beta)/F)$ are isomorphic

Published on 31 Mar 2026 - 23:51

score 208 · Answer 5 · 2021-03-15 12:43:46

208

Views

Showing that $x^5 - 5 a^4 x + a$ is irreducible.

Published on 15 Mar 2021 - 12:43

score 46 · Answer 6 · 2021-03-19 07:25:00

46

Views

Just want to make it clear for the Defintion of Splitting Field

Published on 19 Mar 2021 - 7:25

score 79 · Answer 7 · 2026-03-30 05:26:48

79

Views

Proof that if you have two splitting fields for the same polynomial and one of them is contained in a radical extension, then so is the other one.

Published on 30 Mar 2026 - 5:26

score 207 · Answer 8 · 2021-03-30 22:37:03

207

Views

Finding Splitting Field, Galois Group, Normal Subgroups (Edited)

Published on 30 Mar 2021 - 22:37

score 84 · Answer 9 · 2021-04-04 15:19:48

84

Views

Is there a characterization of fields $k$ such that, if $f\in k[x]$ splits over $k$, so does $f'$?

Published on 04 Apr 2021 - 15:19

score 119 · Answer 10 · 2026-04-02 15:12:49

119

Views

Which real numbers are contained in $\mathbb{Q}(\cos40+i\sin40)$?

Published on 02 Apr 2026 - 15:12

score 101 · Answer 11 · 2021-04-07 23:16:16

101

Views

Find the Galois Group of a field extension

Published on 07 Apr 2021 - 23:16

score 78 · Answer 12 · 2021-04-07 23:20:52

78

Views

How to prove that $\mathbb{Q}(2\cos40, 2\cos80, 2 \cos160)=\mathbb{Q}(\cos(40))$

Published on 07 Apr 2021 - 23:20

score 90 · Answer 13 · 2021-04-12 18:27:31

90

Views

Prove that solvability by radicals does not depend on the choice of splitting field

Published on 12 Apr 2021 - 18:27

score 72 · Answer 14 · 2026-03-30 05:28:55

72

Views

Is there an irreducible quartic over $\mathbb{Q}$ whose splitting field is not radical?

Published on 30 Mar 2026 - 5:28

score 191 · Answer 15 · 2026-03-30 05:26:54

191

Views

Existence of an irreducible quartic polynomial in $\mathbb{Q}[x]$ with four real roots and Galois group $A_4$.

Published on 30 Mar 2026 - 5:26

List Question

Prove or disprove that the rings $R$ and $S$ are isomorphic.

Galois group of polynomial over $\mathbb{Q}(\sqrt{-3})$

Let $f(x) = x^4 + 2x^2 - 6$ and let E be the splitting field of $f(x)$ over $\mathbb{Q}$.

Prove that $|\text{Aut}(F(\alpha)/F)| = |\text{Aut}(F(\beta)/F)|$ and the groups $\text{Aut}(F(\alpha)/F)$ and $\text{Aut}(F(\beta)/F)$ are isomorphic

Showing that $x^5 - 5 a^4 x + a$ is irreducible.

Just want to make it clear for the Defintion of Splitting Field

Proof that if you have two splitting fields for the same polynomial and one of them is contained in a radical extension, then so is the other one.

Finding Splitting Field, Galois Group, Normal Subgroups (Edited)

Is there a characterization of fields $k$ such that, if $f\in k[x]$ splits over $k$, so does $f'$?

Which real numbers are contained in $\mathbb{Q}(\cos40+i\sin40)$?

Find the Galois Group of a field extension

How to prove that $\mathbb{Q}(2\cos40, 2\cos80, 2 \cos160)=\mathbb{Q}(\cos(40))$

Prove that solvability by radicals does not depend on the choice of splitting field

Is there an irreducible quartic over $\mathbb{Q}$ whose splitting field is not radical?

Existence of an irreducible quartic polynomial in $\mathbb{Q}[x]$ with four real roots and Galois group $A_4$.

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