List questions from field-theory

Published on 13 Apr 2026 - 8:12

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Irreducible polynomial over field of characteristic $0$ cannot have multiple zeroes

Published on 13 Apr 2026 - 21:30

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Let $R$ be a ring, and let $V$ denote the $R$-Module $R$. Determine all module homomorphisms (need clarification of some concepts)

Published on 23 Apr 2026 - 5:04

170

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normal and separable extension

Published on 15 Apr 2026 - 3:51

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Every finite field is perfect

Published on 12 Apr 2026 - 8:39

497

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Zeroes of irreducible polynomial over splitting field

Published on 10 Apr 2026 - 21:32

172

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Irreducible polynomial that has a multiple zero example

Published on 13 Apr 2026 - 19:13

203

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$\mathbb{F}_{2^4}$ is not isomorphic to a subring of $\mathbb{F}_{2^5}$

Published on 16 Apr 2026 - 1:47

448

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Minimal polynomial over some different fields

Published on 11 Apr 2026 - 22:01

342

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Is this field extension finite?

Published on 13 Apr 2026 - 22:30

66

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Why is $\mathbb{Z}_n$ a field only if $n$ is prime?

Published on 15 Apr 2026 - 3:57

868

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show it is irreducible over $\mathbb{Q}(\sqrt{2})$ and $\mathbb{Q}(i)$

Published on 14 Apr 2026 - 22:22

597

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Surjectivity of Frobenius Endomorphism

Published on 08 Apr 2026 - 20:10

1.9k

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Irreducibility of polynomials in ring

Published on 13 Apr 2026 - 22:23

234

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A Condition for division ring being a field.

Published on 10 May 2026 - 23:14

List Question

Understanding this theorem indicating the simplicity of a field extension

Irreducible polynomial over field of characteristic $0$ cannot have multiple zeroes

Let $R$ be a ring, and let $V$ denote the $R$-Module $R$. Determine all module homomorphisms (need clarification of some concepts)

normal and separable extension

Every finite field is perfect

Zeroes of irreducible polynomial over splitting field

Irreducible polynomial that has a multiple zero example

$\mathbb{F}_{2^4}$ is not isomorphic to a subring of $\mathbb{F}_{2^5}$

Minimal polynomial over some different fields

Is this field extension finite?

Why is $\mathbb{Z}_n$ a field only if $n$ is prime?

show it is irreducible over $\mathbb{Q}(\sqrt{2})$ and $\mathbb{Q}(i)$

Surjectivity of Frobenius Endomorphism

Irreducibility of polynomials in ring

A Condition for division ring being a field.

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