Question

$K(u,v)=K(u)(v)$ true or false

score 65 · Answer 1 · 2026-04-16 12:25:31

65

Views

$K(u,v)=K(u)(v)$ true or false

Published on 16 Apr 2026 - 12:25

score 109 · Answer 2 · 2026-04-16 04:24:26

109

Views

Polynomial irreducibility over $\mathbb{F} _{7^n}$

Published on 16 Apr 2026 - 4:24

score 88 · Answer 3 · 2026-04-16 04:56:41

88

Views

Quaternion division rings in characteristic $0$

Published on 16 Apr 2026 - 4:56

score 92 · Answer 4 · 2026-04-16 10:41:45

92

Views

If $L/E$ is separable then $L/F$ and $F/E$ are separable

Published on 16 Apr 2026 - 10:41

score 53 · Answer 5 · 2026-04-12 15:08:45

53

Views

Question on the discriminant of a irreducible polynomial

Published on 12 Apr 2026 - 15:08

score 416 · Answer 6 · 2026-04-14 14:49:40

416

Views

What is a "field action", and how does it relate to group actions?

Published on 14 Apr 2026 - 14:49

score 99 · Answer 7 · 2026-04-16 21:17:26

99

Views

For field extension $M/L/K$ with $M/K$ normal, if $\sigma\in\mathrm{Aut}(M/K)$ implies $\sigma(L)\subset M^{\mathrm{Aut}(M/L)}$, must $L/K$ be normal?

Published on 16 Apr 2026 - 21:17

score 97 · Answer 8 · 2026-04-15 03:26:47

97

Views

Generating de Bruijn sequence over Galois fields using primitive polynomial

Published on 15 Apr 2026 - 3:26

score 128 · Answer 9 · 2026-05-11 09:35:32

128

Views

$\left(i\sqrt {\frac{21 \ + \ 5\sqrt{5}}{2}}\right)^n \notin \Bbb{Q}(ζ_{11})$ for all positive integer $n$

Published on 11 May 2026 - 9:35

score 74 · Answer 10 · 2026-04-09 15:24:58

74

Views

How to show that the image of the morphism $X \mapsto X^{p^n}$ equals the separable closure.

Published on 09 Apr 2026 - 15:24

score 90 · Answer 11 · 2026-04-17 08:21:02

90

Views

Galois Group of $\mathbb{Q}(\sqrt 2, \sqrt 3)$

Published on 17 Apr 2026 - 8:21

score 72 · Answer 12 · 2026-04-13 04:13:01

72

Views

Is dependent choice what one must use in this step of Artin's construction of the algebraic closure?

Published on 13 Apr 2026 - 4:13

score 79 · Answer 13 · 2026-04-12 04:00:56

79

Views

Polynomial takes distinct values at set of points

Published on 12 Apr 2026 - 4:00

score 57 · Answer 14 · 2026-04-17 03:46:12

Prove that $\mathbb Q(\sin(θ/3))$ is a finite extension of $\mathbb Q(\sin(θ))$ and compute its degree $[\mathbb Q(\sin(θ/3)):\mathbb Q(\sin(θ))]$.

score 63 · Answer 15 · 2026-04-12 15:43:01

63

Views

How to find a minimal polynomial of $ix$ given the minimal polynomial of $x$

Published on 12 Apr 2026 - 15:43

List Question

$K(u,v)=K(u)(v)$ true or false

Polynomial irreducibility over $\mathbb{F} _{7^n}$

Quaternion division rings in characteristic $0$

If $L/E$ is separable then $L/F$ and $F/E$ are separable

Question on the discriminant of a irreducible polynomial

What is a "field action", and how does it relate to group actions?

For field extension $M/L/K$ with $M/K$ normal, if $\sigma\in\mathrm{Aut}(M/K)$ implies $\sigma(L)\subset M^{\mathrm{Aut}(M/L)}$, must $L/K$ be normal?

Generating de Bruijn sequence over Galois fields using primitive polynomial

$\left(i\sqrt {\frac{21 \ + \ 5\sqrt{5}}{2}}\right)^n \notin \Bbb{Q}(ζ_{11})$ for all positive integer $n$

How to show that the image of the morphism $X \mapsto X^{p^n}$ equals the separable closure.

Galois Group of $\mathbb{Q}(\sqrt 2, \sqrt 3)$

Is dependent choice what one must use in this step of Artin's construction of the algebraic closure?

Polynomial takes distinct values at set of points

Prove that $\mathbb Q(\sin(θ/3))$ is a finite extension of $\mathbb Q(\sin(θ))$ and compute its degree $[\mathbb Q(\sin(θ/3)):\mathbb Q(\sin(θ))]$.

How to find a minimal polynomial of $ix$ given the minimal polynomial of $x$

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