List questions from galois-theory

Published on 17 Mar 2026 - 7:38

77

Views

if $K(a)=K(b)$ are $a$ and $b$ conjugates of the same minimal polynomial in $K[x]$?

Published on 12 Apr 2018 - 4:20

461

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Hilbert 90 and K-forms

Published on 27 Mar 2026 - 2:06

69

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A doubt in understanding a proof in Galois Theory

Published on 25 Mar 2026 - 12:29

68

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Galois group of a splitting field

Published on 12 Apr 2018 - 12:49

34

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Show that $F \not = G$ in splitting field of 2 polynomials over $\mathbb{Q}$

Published on 12 Apr 2018 - 19:00

244

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Can this equation be solved by radicals? $x^6+x^5+2x^4-2x^3-x^2+1=0$

Published on 25 Mar 2026 - 11:03

193

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Confused about part of Milne's notes on the Galois theory of étale algebras over a field

Published on 13 Apr 2018 - 13:01

79

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$K=F(\alpha)$ if $K$ is a quadratic extension

Published on 25 Mar 2026 - 13:59

214

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Corollary 15.3.8 from Artin (degrees of field extensions)

Published on 25 Mar 2026 - 13:56

178

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Proving $\mathbb{Q}(r)$ is Galois over $\mathbb{Q}$ ?

Published on 14 Apr 2018 - 9:04

112

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Find a variety $Y$ such that $k(Y)$ is isomorphic to a given subfield of $k(X)$ for a variety $X$.

Published on 14 Apr 2018 - 15:10

2.2k

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Tower Law and normal field extensions

Published on 25 Mar 2026 - 13:53

138

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Classify all the Galois group of the splitting field of $(x^2-2)(x^2-3)(x^2-5)$

Published on 15 Apr 2018 - 1:38

94

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Let $n \geq 3$ and let $p$ be prime. Show that $\sqrt[n]{p}$ is not contained in a cyclotomic extension of $\mathbb{Q}$

Published on 23 Mar 2026 - 1:40

List Question

Fundamental Algebra Theorem un other fields

if $K(a)=K(b)$ are $a$ and $b$ conjugates of the same minimal polynomial in $K[x]$?

Hilbert 90 and K-forms

A doubt in understanding a proof in Galois Theory

Galois group of a splitting field

Show that $F \not = G$ in splitting field of 2 polynomials over $\mathbb{Q}$

Can this equation be solved by radicals? $x^6+x^5+2x^4-2x^3-x^2+1=0$

Confused about part of Milne's notes on the Galois theory of étale algebras over a field

$K=F(\alpha)$ if $K$ is a quadratic extension

Corollary 15.3.8 from Artin (degrees of field extensions)

Proving $\mathbb{Q}(r)$ is Galois over $\mathbb{Q}$ ?

Find a variety $Y$ such that $k(Y)$ is isomorphic to a given subfield of $k(X)$ for a variety $X$.

Tower Law and normal field extensions

Classify all the Galois group of the splitting field of $(x^2-2)(x^2-3)(x^2-5)$

Let $n \geq 3$ and let $p$ be prime. Show that $\sqrt[n]{p}$ is not contained in a cyclotomic extension of $\mathbb{Q}$

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