List questions from extension-field

Published on 21 Apr 2019 - 19:42

50

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If $[K:\Bbb{Q}]=2$ then $K=\Bbb{Q}(\sqrt{d})$.

Published on 28 Mar 2026 - 3:02

1.2k

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Proving that a field extension is Galois

Published on 28 Mar 2026 - 1:02

147

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Let $F = Z_5[x]/(x^3-x^2-1) = Z_5(u)$ where $u = [x]$ Give a basis for $F$ over $Z_5$

Published on 26 Apr 2019 - 17:51

279

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What is the tower of fields a number must be in in order to be constructed by MARKED RULER and compass?

Published on 26 Mar 2026 - 3:01

274

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What does it mean for a field to be generated by some set of elements?

Published on 31 Mar 2026 - 3:35

173

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Prove that $E=\Bbb Q(\sqrt[d]{a})$

Published on 27 Mar 2026 - 22:19

394

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Minimal polynomial of extension of degree 2 over a finite field with characteristic 2

Published on 29 Mar 2026 - 3:36

320

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Degree of splitting field of $x^3-5$ over $\mathbb{F}_7$

Published on 25 Mar 2026 - 23:52

86

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Any element in $K/\mathbb Q_p$ can be generated by some $\pi \in K$

Published on 25 Mar 2026 - 7:43

348

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Doubts regarding 'quadratic field can be obtained by adjoining square root'

Published on 03 May 2019 - 11:22

94

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tamely totally ramified extensions and the equation $x^e-pu=0$

Published on 26 Mar 2026 - 23:09

888

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Show that an extension $K/F$ with $|K:F| = 2$ is normal.

Published on 25 Mar 2026 - 6:39

309

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Find the Addition and Multiplication tables for GF(7)

Published on 05 May 2019 - 6:28

48

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$F\subseteq E\subseteq M$ is finite field extensions, if $M/F$ is normal then $M/E$ is normal

Published on 23 Feb 2026 - 1:05

List Question

A question on the Galois correspondance of $\sigma^2$ in $D_8$.

If $[K:\Bbb{Q}]=2$ then $K=\Bbb{Q}(\sqrt{d})$.

Proving that a field extension is Galois

Let $F = Z_5[x]/(x^3-x^2-1) = Z_5(u)$ where $u = [x]$ Give a basis for $F$ over $Z_5$

What is the tower of fields a number must be in in order to be constructed by MARKED RULER and compass?

What does it mean for a field to be generated by some set of elements?

Prove that $E=\Bbb Q(\sqrt[d]{a})$

Minimal polynomial of extension of degree 2 over a finite field with characteristic 2

Degree of splitting field of $x^3-5$ over $\mathbb{F}_7$

Any element in $K/\mathbb Q_p$ can be generated by some $\pi \in K$

Doubts regarding 'quadratic field can be obtained by adjoining square root'

tamely totally ramified extensions and the equation $x^e-pu=0$

Show that an extension $K/F$ with $|K:F| = 2$ is normal.

Find the Addition and Multiplication tables for GF(7)

$F\subseteq E\subseteq M$ is finite field extensions, if $M/F$ is normal then $M/E$ is normal

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