List questions from extension-field

Published on 18 Jan 2017 - 20:40

276

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Field extension exercise

Published on 19 Jan 2017 - 0:54

122

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$\mathbb{F}$ contains a unique subfield of cardinality $p^n$

Published on 19 Jan 2017 - 16:45

526

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Difference between normal extension and splitting extension

Published on 27 Mar 2026 - 4:15

37

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Let $L|K$ be an extension with $[L:K]=2$. Show that $\tau(\mu + \nu \alpha) = \mu - \nu\alpha$ defines an automorphism of $L$ that fixes $K$

Published on 19 Jan 2017 - 18:37

260

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Two different (isomorphic) splitting field

Published on 27 Mar 2026 - 4:14

214

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Field extensions and Galois goup

Published on 20 Jan 2017 - 23:08

188

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One definition about field extension

Published on 21 Jan 2017 - 22:50

163

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Why is irreducible $x^{3n}+x^2y+xy^2+y$ in $\mathbb{Q}[x,y]$?

Published on 02 Apr 2026 - 21:18

183

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Given a complete discrete valuation field $L$, is there always a complete local field $K\subset L$?

Published on 26 Mar 2026 - 13:51

116

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Find a primitive element for the extension $\mathbb Q(i,\sqrt3,e^{{\pi i/4}})/\mathbb Q$.

Published on 24 Jan 2017 - 1:03

5.7k

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Finding a Galois extension of $\Bbb Q$ of degree $3$

Published on 24 Jan 2017 - 20:16

454

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Are these simple field extensions normal?

Published on 25 Jan 2017 - 12:58

272

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Writing elements of field extension in terms of minimal polynomial

Published on 26 Jan 2017 - 4:00

137

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Example of quadratic extension

Published on 26 Jan 2017 - 20:45

List Question

How to find a polynomial of which this field is a splitting field?

Field extension exercise

$\mathbb{F}$ contains a unique subfield of cardinality $p^n$

Difference between normal extension and splitting extension

Let $L|K$ be an extension with $[L:K]=2$. Show that $\tau(\mu + \nu \alpha) = \mu - \nu\alpha$ defines an automorphism of $L$ that fixes $K$

Two different (isomorphic) splitting field

Field extensions and Galois goup

One definition about field extension

Why is irreducible $x^{3n}+x^2y+xy^2+y$ in $\mathbb{Q}[x,y]$?

Given a complete discrete valuation field $L$, is there always a complete local field $K\subset L$?

Find a primitive element for the extension $\mathbb Q(i,\sqrt3,e^{{\pi i/4}})/\mathbb Q$.

Finding a Galois extension of $\Bbb Q$ of degree $3$

Are these simple field extensions normal?

Writing elements of field extension in terms of minimal polynomial

Example of quadratic extension

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