Question

Minimum polynomial of generator of finite extension

score 54 · Answer 1 · 2026-04-05 11:04:21

54

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Minimum polynomial of generator of finite extension

Published on 05 Apr 2026 - 11:04

score 53 · Answer 2 · 2023-03-09 22:24:12

53

Views

If $L/K$ is a field extension and $K$ is countable, if $[L:K]$ is finite then $L$ is countable

Published on 09 Mar 2023 - 22:24

score 55 · Answer 3 · 2026-03-27 00:06:43

55

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Proving that this kind of matrix ring is left Noetherian but not right Noetherian

Published on 27 Mar 2026 - 0:06

score 96 · Answer 4 · 2026-02-23 01:08:07

96

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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 23 Feb 2026 - 1:08

score 88 · Answer 5 · 2026-03-27 10:46:09

88

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

Published on 27 Mar 2026 - 10:46

score 70 · Answer 6 · 2026-03-29 10:19:23

70

Views

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

Published on 29 Mar 2026 - 10:19

score 54 · Answer 7 · 2023-03-12 22:35:12

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 94 · Answer 8 · 2026-04-05 11:03:47

94

Views

Proving this polynomial is in $ K[X]$

Published on 05 Apr 2026 - 11:03

score 183 · Answer 9 · 2026-04-06 08:17:06

183

Views

Residue field of DVR

Published on 06 Apr 2026 - 8:17

score 40 · Answer 10 · 2026-03-26 02:57:43

40

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Possible failure of $ef=n$ for a degree $n$ extension of a field complete to a nondiscrete nonarchimedean valuation?

Published on 26 Mar 2026 - 2:57

score 165 · Answer 11 · 2026-03-26 17:53:15

165

Views

Tensor of ring of formal power series and a field

Published on 26 Mar 2026 - 17:53

score 45 · Answer 12 · 2026-03-29 05:44:11

45

Views

Suppose $K$ is a field such that every finite Galois extension of $K$ is cyclic. Is there a name for this property?

Published on 29 Mar 2026 - 5:44

score 93 · Answer 13 · 2023-03-20 00:00:57

93

Views

Is $\alpha = \pi^2$ algebraic over $\mathbb{Q}(\pi)$?

Published on 20 Mar 2023 - 0:00

score 169 · Answer 14 · 2023-03-20 16:43:04

169

Views

Find the possible values for $[\mathbb{Q}(\alpha,\beta):\mathbb{Q}]$ and provide an example of $(\alpha,\beta)$ for each possible value

Published on 20 Mar 2023 - 16:43

score 118 · Answer 15 · 2026-03-26 19:11:46

118

Views

Find a Galois extension whose Galois group is $\mathbb{Z}_4 \times \mathbb{Z}_4$

Published on 26 Mar 2026 - 19:11

List Question

Minimum polynomial of generator of finite extension

If $L/K$ is a field extension and $K$ is countable, if $[L:K]$ is finite then $L$ is countable

Proving that this kind of matrix ring is left Noetherian but not right Noetherian

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?

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?

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

Proving this polynomial is in $ K[X]$

Residue field of DVR

Possible failure of $ef=n$ for a degree $n$ extension of a field complete to a nondiscrete nonarchimedean valuation?

Tensor of ring of formal power series and a field

Suppose $K$ is a field such that every finite Galois extension of $K$ is cyclic. Is there a name for this property?

Is $\alpha = \pi^2$ algebraic over $\mathbb{Q}(\pi)$?

Find the possible values for $[\mathbb{Q}(\alpha,\beta):\mathbb{Q}]$ and provide an example of $(\alpha,\beta)$ for each possible value

Find a Galois extension whose Galois group is $\mathbb{Z}_4 \times \mathbb{Z}_4$

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