List questions from field-theory

Published on 25 Mar 2026 - 9:47

235

Views

Find number of polynomials in $P_n(F)$ where $F$ is a finite field with cardinality $m$.

Published on 27 Mar 2026 - 0:06

705

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Is $F_p (X,Y)$ a simple extension over $F_p (X^p,Y^p)$?

Published on 29 Mar 2026 - 8:15

357

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Showing that the Galois group has an element of order 8.

Published on 25 Mar 2026 - 14:47

130

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Proof Check: Two well-ordered algebraic closures of a field $F$ are isomorphic (without Zorn's Lemma)

Published on 16 Aug 2018 - 16:25

96

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Avoiding normal closures in proving a characterization of normal extensions

Published on 29 Mar 2026 - 10:14

35

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Given a field extension E/F, $f(x)\in E[x]$, and $f(\alpha )\in F, \forall \alpha \in F$. Does $f(x)\in F[x]$?

Published on 29 Mar 2026 - 8:15

185

Views

What's remarkable about this transfer of structure from $\Bbb Z[\frac12]$ to $\Bbb C$?

Published on 25 Mar 2026 - 16:13

222

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Purely Inseparable Field Extension Differentials

Published on 27 Mar 2026 - 8:39

211

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There are not $n$-th and $m$-th primitive roots of the unity, where $n$ and $m$ are coprime numbers.

Published on 19 Aug 2018 - 21:36

68

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Is $\mathbb{Z}_p(y)$ a field, where $y$ is an indeterminate/placeholder?

Published on 29 Mar 2026 - 8:21

482

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Similarity of matrix over field extension

Published on 20 Aug 2018 - 7:25

73

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Primitive Element and other roots of its minimal polynomial

Published on 29 Mar 2026 - 10:18

75

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What does this exercise from field theory really tell us?

Published on 25 Mar 2026 - 1:35

991

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Galois group of $x^3-3x-1$ over $\mathbb{Q}$

Published on 27 Mar 2026 - 13:24

List Question

Continuity of trace and norm

Find number of polynomials in $P_n(F)$ where $F$ is a finite field with cardinality $m$.

Is $F_p (X,Y)$ a simple extension over $F_p (X^p,Y^p)$?

Showing that the Galois group has an element of order 8.

Proof Check: Two well-ordered algebraic closures of a field $F$ are isomorphic (without Zorn's Lemma)

Avoiding normal closures in proving a characterization of normal extensions

Given a field extension E/F, $f(x)\in E[x]$, and $f(\alpha )\in F, \forall \alpha \in F$. Does $f(x)\in F[x]$?

What's remarkable about this transfer of structure from $\Bbb Z[\frac12]$ to $\Bbb C$?

Purely Inseparable Field Extension Differentials

There are not $n$-th and $m$-th primitive roots of the unity, where $n$ and $m$ are coprime numbers.

Is $\mathbb{Z}_p(y)$ a field, where $y$ is an indeterminate/placeholder?

Similarity of matrix over field extension

Primitive Element and other roots of its minimal polynomial

What does this exercise from field theory really tell us?

Galois group of $x^3-3x-1$ over $\mathbb{Q}$

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