List questions from extension-field

Published on 05 Dec 2016 - 6:07

424

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Intermediate Radical Extension Paradox

Published on 03 Apr 2026 - 19:12

1.5k

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The simplest radical extension with a non-radical subextension

Published on 06 Dec 2016 - 4:19

294

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Degree of Field Extension of Number Fields

Published on 06 Dec 2016 - 19:07

411

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Set of elements fixed by Galois group of $E$ over $F$ if $F$ (requesting alternate proof)

Published on 27 Mar 2026 - 2:37

193

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Deciding whether Galois group is $C_6$ or $S_3$

Published on 09 Dec 2016 - 0:32

82

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A polynomial that is reducible under every finite field?

Published on 03 Apr 2026 - 21:45

44

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Clarification prove that $F(a) = F(a^2)$.

Published on 10 Dec 2016 - 21:32

979

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Alternative way to show $\sqrt{2}+ \sqrt{3}$ is algebraic over $\mathbb{Q}$ of degree 4.

Published on 10 Dec 2016 - 23:58

94

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What Exactly is the Difference Between $F[\alpha$] and $F(\alpha$)?

Published on 11 Dec 2016 - 8:49

884

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Basis for a Field Extension

Published on 12 Dec 2016 - 10:56

832

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Simple Extensions Explained?

Published on 12 Dec 2016 - 11:35

3.2k

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Transitivity of Algebraic Field Extensions

Published on 12 Dec 2016 - 12:45

43

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Clarification for Extension Fields and Galois Field

Published on 03 Apr 2026 - 23:20

69

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Algebraic extension over field $F$

Published on 14 Dec 2016 - 17:09

List Question

Zero of $x^2 + 1$ in $\mathbb{Q}[x] / \langle (x^2 + 1)\rangle$

Intermediate Radical Extension Paradox

The simplest radical extension with a non-radical subextension

Degree of Field Extension of Number Fields

Set of elements fixed by Galois group of $E$ over $F$ if $F$ (requesting alternate proof)

Deciding whether Galois group is $C_6$ or $S_3$

A polynomial that is reducible under every finite field?

Clarification prove that $F(a) = F(a^2)$.

Alternative way to show $\sqrt{2}+ \sqrt{3}$ is algebraic over $\mathbb{Q}$ of degree 4.

What Exactly is the Difference Between $F[\alpha$] and $F(\alpha$)?

Basis for a Field Extension

Simple Extensions Explained?

Transitivity of Algebraic Field Extensions

Clarification for Extension Fields and Galois Field

Algebraic extension over field $F$

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