List questions from extension-field

Published on 14 Apr 2026 - 5:03

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algebraic integers in quadratic field

Published on 15 Apr 2026 - 9:57

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Field not closed under complex conjugation

Published on 14 Apr 2026 - 0:24

473

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Prove field extension is a field

Published on 14 Apr 2026 - 1:20

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Dimension of $K\subset L(\alpha)$ where $L$ is a field extension of $K$

Published on 16 Apr 2026 - 5:03

190

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Subfield of $\mathbb R$ with algebraic closure as $\mathbb C$.

Published on 15 Apr 2026 - 9:25

304

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Integral Closure in an Unramified Extension is Generated by a Single Element

Published on 13 Apr 2026 - 0:24

832

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Characterizing Galois field extensions via tensor product

Published on 11 Apr 2026 - 21:51

545

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Proof that $K\otimes_F L$ is not noetherian

Published on 11 Apr 2026 - 1:05

334

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Simple field extension inequality proof

Published on 16 Apr 2026 - 6:49

74

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Size of field extension is at most $p^d$

Published on 21 Apr 2026 - 16:44

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Exercise about field extensions

Published on 12 Apr 2026 - 5:23

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A counterexample about an inequality- Field extensions

Published on 10 Apr 2026 - 17:44

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How to show that any field extension $K/\mathbb{Q}$ of degree 4 that is not Galois has a quadratic extension $L$ that is Galois over $\mathbb{Q}$.

Published on 13 Apr 2026 - 23:01

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Computing basis of a field extension

Published on 14 Apr 2026 - 18:08

List Question

Make Galois extension large enough to let Galois group act trivially on module

algebraic integers in quadratic field

Field not closed under complex conjugation

Prove field extension is a field

Dimension of $K\subset L(\alpha)$ where $L$ is a field extension of $K$

Subfield of $\mathbb R$ with algebraic closure as $\mathbb C$.

Integral Closure in an Unramified Extension is Generated by a Single Element

Characterizing Galois field extensions via tensor product

Proof that $K\otimes_F L$ is not noetherian

Simple field extension inequality proof

Size of field extension is at most $p^d$

Exercise about field extensions

A counterexample about an inequality- Field extensions

How to show that any field extension $K/\mathbb{Q}$ of degree 4 that is not Galois has a quadratic extension $L$ that is Galois over $\mathbb{Q}$.

Computing basis of a field extension

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