Question

Find a degree 3 polynomial that has a galois group of the extension field which is isomorfic to the ciclic group of order 3.

score 55 · Answer 1 · 2023-03-31 20:56:46

55

Views

Find a degree 3 polynomial that has a galois group of the extension field which is isomorfic to the ciclic group of order 3.

Published on 31 Mar 2023 - 20:56

score 304 · Answer 2 · 2023-04-01 20:56:22

304

Views

How to find a $\mathbb{Q}$-basis for the splitting field of $x^4-2$ over $\mathbb{Q}$?

Published on 01 Apr 2023 - 20:56

score 64 · Answer 3 · 2023-04-08 05:17:38

64

Views

Is $g(x)$ reducible in $k[x]$?

Published on 08 Apr 2023 - 5:17

score 120 · Answer 4 · 2023-04-08 12:58:20

120

Views

If $K$ is a splitting field of $f\in F[x]$, is $F(\alpha)$ a splitting field of $f/(x - \alpha)$?

Published on 08 Apr 2023 - 12:58

score 63 · Answer 5 · 2023-04-14 18:05:29

63

Views

Splitting field of $x^4+64$ over $\mathbb{Q}$

Published on 14 Apr 2023 - 18:05

score 168 · Answer 6 · 2023-04-16 18:17:55

168

Views

Splitting field of $x^3 +x +1$ over $\mathbb F_{11}$

Published on 16 Apr 2023 - 18:17

score 291 · Answer 7 · 2023-04-17 21:21:06

291

Views

Degree of splitting field of a polynomial over $\mathbb F_2$

Published on 17 Apr 2023 - 21:21

score 161 · Answer 8 · 2023-04-19 05:44:52

161

Views

Determining the automorphism group of the splitting field for $x^4-2x^2-\sqrt{2}$ over $\mathbb{Q}(\sqrt{2})$

Published on 19 Apr 2023 - 5:44

score 45 · Answer 9 · 2023-04-23 21:50:13

45

Views

Relation between number of roots of a polynomial and number of cosets of some subgroups of Galois group

Published on 23 Apr 2023 - 21:50

score 159 · Answer 10 · 2023-05-14 01:39:57

159

Views

How does $x^5-5$ factor over $\mathbb{F}_p$ for different values of $p$ mod 5?

Published on 14 May 2023 - 1:39

score 71 · Answer 11 · 2026-02-23 08:32:46

71

Views

If $L/K$ is normal extension $\Rightarrow K_s/K$ is normal extension

Published on 23 Feb 2026 - 8:32

score 41 · Answer 12 · 2023-05-16 20:43:50

41

Views

Question about Splitting Field Extensions

Published on 16 May 2023 - 20:43

score 86 · Answer 13 · 2023-05-23 05:04:53

86

Views

On the definition of algebraic closure

Published on 23 May 2023 - 5:04

score 57 · Answer 14 · 2023-05-31 01:15:50

57

Views

Determining intermediate fields of the splitting field of $x^3-3\in \mathbb{Q}[X]$ over $\mathbb{Q}$

Published on 31 May 2023 - 1:15

score 84 · Answer 15 · 2023-06-06 23:18:21

84

Views

How does the Galois group of a splitting field act on a specific element?

Published on 06 Jun 2023 - 23:18

List Question

Find a degree 3 polynomial that has a galois group of the extension field which is isomorfic to the ciclic group of order 3.

How to find a $\mathbb{Q}$-basis for the splitting field of $x^4-2$ over $\mathbb{Q}$?

Is $g(x)$ reducible in $k[x]$?

If $K$ is a splitting field of $f\in F[x]$, is $F(\alpha)$ a splitting field of $f/(x - \alpha)$?

Splitting field of $x^4+64$ over $\mathbb{Q}$

Splitting field of $x^3 +x +1$ over $\mathbb F_{11}$

Degree of splitting field of a polynomial over $\mathbb F_2$

Determining the automorphism group of the splitting field for $x^4-2x^2-\sqrt{2}$ over $\mathbb{Q}(\sqrt{2})$

Relation between number of roots of a polynomial and number of cosets of some subgroups of Galois group

How does $x^5-5$ factor over $\mathbb{F}_p$ for different values of $p$ mod 5?

If $L/K$ is normal extension $\Rightarrow K_s/K$ is normal extension

Question about Splitting Field Extensions

On the definition of algebraic closure

Determining intermediate fields of the splitting field of $x^3-3\in \mathbb{Q}[X]$ over $\mathbb{Q}$

How does the Galois group of a splitting field act on a specific element?

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