List questions from extension-field

Published on 04 Nov 2014 - 18:44

143

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Galois extensions questions

Published on 04 Nov 2014 - 19:29

84

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$E$ is a splitting field of $f(x)$

Published on 26 Mar 2026 - 6:29

137

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Prove $\sqrt{-7} \not\in \mathbb{Z}\left[\frac{2+3\sqrt{-7}}{4}\right]$

Published on 05 Nov 2014 - 15:39

741

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Algebraic closed field has infinite many elements

Published on 07 Nov 2014 - 0:16

204

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Find the degree of field extension

Published on 28 Mar 2026 - 11:33

939

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Degree of an algebraic number over a field

Published on 07 Nov 2014 - 19:20

2.6k

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Finding all intermediate fields

Published on 07 Nov 2014 - 20:07

137

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If the degree of $\alpha=5555$, what is the degree of $\alpha^2$?

Published on 08 Nov 2014 - 13:50

1k

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If $F/k$ normal, $g,h \in F[X]$ monic irreducible factors of $f \in k[X]$, then $\exists\ \sigma \in Aut(F/k)$ s.t. $g^\sigma = h$.

Published on 23 Feb 2026 - 1:08

1.6k

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Calculating automorphism groups

Published on 09 Nov 2014 - 21:24

400

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Do we know if all simple extensions of the field of rational numbers by transcendental numbers are not equal?

Published on 26 Mar 2026 - 2:57

637

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Can a field be isomorphic to its subfield but not to a subfield in between?

Published on 10 Nov 2014 - 22:20

3.8k

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Is Q(4th root(2))/Q a galois extension

Published on 11 Nov 2014 - 20:59

312

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Prove that $\mathbb{Q}[\sqrt{p}]$ is a field between $\mathbb{Q}$ and $\mathbb{R}$

Published on 30 Mar 2026 - 2:05

List Question

The exponential extension of $\mathbb{Q}$ is a proper subset of $\mathbb{C}$?

Galois extensions questions

$E$ is a splitting field of $f(x)$

Prove $\sqrt{-7} \not\in \mathbb{Z}\left[\frac{2+3\sqrt{-7}}{4}\right]$

Algebraic closed field has infinite many elements

Find the degree of field extension

Degree of an algebraic number over a field

Finding all intermediate fields

If the degree of $\alpha=5555$, what is the degree of $\alpha^2$?

If $F/k$ normal, $g,h \in F[X]$ monic irreducible factors of $f \in k[X]$, then $\exists\ \sigma \in Aut(F/k)$ s.t. $g^\sigma = h$.

Calculating automorphism groups

Do we know if all simple extensions of the field of rational numbers by transcendental numbers are not equal?

Can a field be isomorphic to its subfield but not to a subfield in between?

Is Q(4th root(2))/Q a galois extension

Prove that $\mathbb{Q}[\sqrt{p}]$ is a field between $\mathbb{Q}$ and $\mathbb{R}$

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