Question

Odd field extensions, possible?

score 57 · Answer 1 · 2022-05-26 19:13:58

57

Views

Odd field extensions, possible?

Published on 26 May 2022 - 19:13

score 341 · Answer 2 · 2022-05-27 18:50:55

341

Views

Choosing splitting field of $x^4+x^2+1$ over $\mathbb{Q}$

Published on 27 May 2022 - 18:50

score 53 · Answer 3 · 2022-05-28 06:46:17

53

Views

Confusion regarding a proof in Galois theory.

Published on 28 May 2022 - 6:46

score 122 · Answer 4 · 2022-05-30 18:45:03

122

Views

Given quintic polynomial $f$ - If ${\rm Gal}(f)$ has an element of order 3 then it is not solvable

Published on 30 May 2022 - 18:45

score 132 · Answer 5 · 2022-06-04 05:40:47

132

Views

Some questions on polynomial $f(x)=x^4+x^2+4$ over $\mathbb{Q}$

Published on 04 Jun 2022 - 5:40

score 132 · Answer 6 · 2022-06-04 14:42:36

132

Views

Splitting field of $x^8-1$ over $\mathbb{F}_2 ,\mathbb{F}_3,\mathbb{F}_{16}$

Published on 04 Jun 2022 - 14:42

score 68 · Answer 7 · 2022-06-05 17:47:25

68

Views

Confusing question on $\mathbb{Z}_4$ and the polynomial $x^2+x+1$

Published on 05 Jun 2022 - 17:47

score 40 · Answer 8 · 2022-06-08 08:46:45

40

Views

Finding roots of polynomial over $\mathbb{Q}$ satisfying isomorphism

Published on 08 Jun 2022 - 8:46

score 251 · Answer 9 · 2026-02-23 08:24:58

251

Views

Root of the polynomial $x^3-x-1$ over $\mathbb{Q}$ does not generate normal extension

Published on 23 Feb 2026 - 8:24

score 86 · Answer 10 · 2026-03-30 17:09:59

86

Views

Fundamental Thm of Galois Theory: Showing that $L^H$ is normal over $F$ iff $H$ is normal in $G$

Published on 30 Mar 2026 - 17:09

score 51 · Answer 11 · 2022-06-14 16:42:15

51

Views

Splitting field of a torus is the splitting fields of the polynomials defining the torus?

Published on 14 Jun 2022 - 16:42

score 64 · Answer 12 · 2026-03-30 17:13:12

64

Views

Sub-fields of $\mathbb{Q}(a)$ ,$a=\sqrt{4+\sqrt{15}}$ using Galois theory.

Published on 30 Mar 2026 - 17:13

score 72 · Answer 13 · 2022-06-22 03:29:32

72

Views

Intermediate Fields of Rational Functions

Published on 22 Jun 2022 - 3:29

score 86 · Answer 14 · 2022-07-03 00:56:31

86

Views

Find the splitting field of the polynomial $x^4-4$ over $\mathbb{Q}$ and the structure of the Galois Group.

Published on 03 Jul 2022 - 0:56

score 55 · Answer 15 · 2022-07-19 22:40:12

55

Views

Let $L$ be the splitting field of the polynomial $x^4-2x^2-1$ above $\mathbb{Q}$, Calculate $G(L,\mathbb{Q})$.

Published on 19 Jul 2022 - 22:40

List Question

Odd field extensions, possible?

Choosing splitting field of $x^4+x^2+1$ over $\mathbb{Q}$

Confusion regarding a proof in Galois theory.

Given quintic polynomial $f$ - If ${\rm Gal}(f)$ has an element of order 3 then it is not solvable

Some questions on polynomial $f(x)=x^4+x^2+4$ over $\mathbb{Q}$

Splitting field of $x^8-1$ over $\mathbb{F}_2 ,\mathbb{F}_3,\mathbb{F}_{16}$

Confusing question on $\mathbb{Z}_4$ and the polynomial $x^2+x+1$

Finding roots of polynomial over $\mathbb{Q}$ satisfying isomorphism

Root of the polynomial $x^3-x-1$ over $\mathbb{Q}$ does not generate normal extension

Fundamental Thm of Galois Theory: Showing that $L^H$ is normal over $F$ iff $H$ is normal in $G$

Splitting field of a torus is the splitting fields of the polynomials defining the torus?

Sub-fields of $\mathbb{Q}(a)$ ,$a=\sqrt{4+\sqrt{15}}$ using Galois theory.

Intermediate Fields of Rational Functions

Find the splitting field of the polynomial $x^4-4$ over $\mathbb{Q}$ and the structure of the Galois Group.

Let $L$ be the splitting field of the polynomial $x^4-2x^2-1$ above $\mathbb{Q}$, Calculate $G(L,\mathbb{Q})$.

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