List questions from extension-field

Published on 27 Mar 2026 - 17:21

892

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Showing this field extension is not normal

Published on 24 Nov 2014 - 17:52

1.8k

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Show that it is/is not a normal extension

Published on 24 Nov 2014 - 21:25

105

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Cyclotomic Extensions and Minimal Polynomials

Published on 24 Nov 2014 - 23:34

138

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Why $F[x]/p(x)$ would contain $F$?

Published on 25 Nov 2014 - 0:27

196

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Proof or counterexample: If $F\subseteq K$ and $r\in K$. If $[F(r):F]=4$ then $F(r)=F(r^3)$.

Published on 01 Apr 2026 - 12:53

107

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Dimension Field True/False.

Published on 01 Apr 2026 - 12:47

135

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Showing $\mathbf Q(\sqrt2,\mathrm i)=\mathbf Q( \sqrt2+\mathrm i)$.

Published on 25 Nov 2014 - 15:23

1.4k

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Show that an extension is separable

Published on 25 Nov 2014 - 19:57

1.1k

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Galois group of a polynomial and subfields

Published on 26 Nov 2014 - 3:47

202

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Finding whether a field extension is normal and/or separable

Published on 26 Nov 2014 - 11:36

2.1k

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Degree of field extension is infinite

Published on 26 Nov 2014 - 12:53

573

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Galois group of $f = x^5 - 2x^3 - x^2 + 2$

Published on 26 Nov 2014 - 14:49

560

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Basis for field extension $\mathbb{Q}(\zeta , \sqrt[3]{2})/\mathbb{Q}$

Published on 26 Nov 2014 - 15:29

639

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Field of rational functions over $\mathbb{F}_p$

Published on 26 Nov 2014 - 20:14

List Question

Determine sign of sum of square roots

Showing this field extension is not normal

Show that it is/is not a normal extension

Cyclotomic Extensions and Minimal Polynomials

Why $F[x]/p(x)$ would contain $F$?

Proof or counterexample: If $F\subseteq K$ and $r\in K$. If $[F(r):F]=4$ then $F(r)=F(r^3)$.

Dimension Field True/False.

Showing $\mathbf Q(\sqrt2,\mathrm i)=\mathbf Q( \sqrt2+\mathrm i)$.

Show that an extension is separable

Galois group of a polynomial and subfields

Finding whether a field extension is normal and/or separable

Degree of field extension is infinite

Galois group of $f = x^5 - 2x^3 - x^2 + 2$

Basis for field extension $\mathbb{Q}(\zeta , \sqrt[3]{2})/\mathbb{Q}$

Field of rational functions over $\mathbb{F}_p$

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