List questions from extension-field

Published on 11 Apr 2026 - 1:51

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The elementary symmetric functions are a homogeneous system of parameters for the invariant ring of a permutation representation

Published on 26 Mar 2026 - 14:34

407

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Finite Inseparable Extension

Published on 11 Apr 2026 - 8:45

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Prove the extension to be a Galois Extension

Published on 02 Apr 2015 - 19:52

62

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$[\mathbb{F}:\mathbb{K}]=1$ if and only if $\mathbb{F}=\mathbb{K}$.

Published on 02 Apr 2015 - 19:59

81

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Cyclotomic polynomial, after adjoining a radical

Published on 10 Apr 2026 - 18:53

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Element of that $\mathbb Q[\sqrt{2}]$ have a square root in $\mathbb Q[\sqrt{2}]$

Published on 03 Apr 2015 - 17:24

202

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Minimal polynomial problem

Published on 10 Apr 2026 - 22:15

105

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If L/K is algebraic field extension, is L(B)/K(B) also algebraic?

Published on 04 Apr 2015 - 3:35

75

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A question on on field extensions and minimal polynomial

Published on 11 Apr 2026 - 7:19

236

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Dimension of union of fields over intersection of fields.

Published on 04 Apr 2015 - 20:34

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Is every isomorphism of an algebraically closed field onto one of its subfields an automorphism?

Published on 04 Apr 2015 - 21:01

109

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Automorphism in splitting field

Published on 27 Mar 2026 - 18:48

1.2k

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If field $K/F$ is generated by the $\alpha_1,...,\alpha_n$, then an $\sigma\in $ Aut$(K/F)$ of $K$ uniquely determined

Published on 05 Apr 2015 - 20:52

1.1k

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Determine whether the extension is Galois

Published on 27 Mar 2026 - 20:31

List Question

Construct the rule in fields extensions

The elementary symmetric functions are a homogeneous system of parameters for the invariant ring of a permutation representation

Finite Inseparable Extension

Prove the extension to be a Galois Extension

$[\mathbb{F}:\mathbb{K}]=1$ if and only if $\mathbb{F}=\mathbb{K}$.

Cyclotomic polynomial, after adjoining a radical

Element of that $\mathbb Q[\sqrt{2}]$ have a square root in $\mathbb Q[\sqrt{2}]$

Minimal polynomial problem

If L/K is algebraic field extension, is L(B)/K(B) also algebraic?

A question on on field extensions and minimal polynomial

Dimension of union of fields over intersection of fields.

Is every isomorphism of an algebraically closed field onto one of its subfields an automorphism?

Automorphism in splitting field

If field $K/F$ is generated by the $\alpha_1,...,\alpha_n$, then an $\sigma\in $ Aut$(K/F)$ of $K$ uniquely determined

Determine whether the extension is Galois

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