List questions from extension-field

Published on 16 Apr 2026 - 13:17

130

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$\Bbb{Q}(\sqrt{2})$ is a field extension of $\Bbb{Q}$.

Published on 15 Apr 2026 - 21:06

506

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Examples for completions of number fields

Published on 14 Apr 2026 - 21:20

396

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Extension $K$ of field $F$ forms a vector space over $F$

Published on 16 Apr 2026 - 14:18

147

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Prove that $F(\alpha)\cong F[x]/(m_\alpha(x))$.

Published on 15 Apr 2026 - 19:01

58

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How to understand $\mathbb{Z}_2[x]/\left\langle x^3+x+1\right\rangle $

Published on 15 Apr 2026 - 7:18

275

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Degree of a field extension by a transcendental element

Published on 17 Apr 2026 - 0:28

581

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Given a field $\mathbb F$, is there a smallest field $\mathbb G\supseteq\mathbb F$ where every element in $\mathbb G$ has an $n$th root for all $n$?

Published on 16 Apr 2026 - 2:55

69

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Multiplicites of roots of $x^{p^k}-x$ ($p$ is prime) in $L[x]$ with $L$ as an extension of $Z_p$

Published on 17 Apr 2026 - 8:22

64

Views

Normal, Non Separable field extension which is not Simple

Published on 14 Apr 2026 - 4:14

32

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Existence of isomorphism in field extension

Published on 12 Apr 2026 - 17:39

63

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Finding subfields of a field extension and help with the definition

Published on 11 Apr 2026 - 7:31

66

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Conjugates in Field Theory

Published on 25 Mar 2026 - 21:31

51

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Completion of a field at some point

Published on 15 Apr 2026 - 5:21

62

Views

Computation in a Quotient Ring

Published on 16 Apr 2026 - 0:45

List Question

Intersection of two extensions of $\mathbb{Q}$

$\Bbb{Q}(\sqrt{2})$ is a field extension of $\Bbb{Q}$.

Examples for completions of number fields

Extension $K$ of field $F$ forms a vector space over $F$

Prove that $F(\alpha)\cong F[x]/(m_\alpha(x))$.

How to understand $\mathbb{Z}_2[x]/\left\langle x^3+x+1\right\rangle $

Degree of a field extension by a transcendental element

Given a field $\mathbb F$, is there a smallest field $\mathbb G\supseteq\mathbb F$ where every element in $\mathbb G$ has an $n$th root for all $n$?

Multiplicites of roots of $x^{p^k}-x$ ($p$ is prime) in $L[x]$ with $L$ as an extension of $Z_p$

Normal, Non Separable field extension which is not Simple

Existence of isomorphism in field extension

Finding subfields of a field extension and help with the definition

Conjugates in Field Theory

Completion of a field at some point

Computation in a Quotient Ring

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