List questions from field-theory

Published on 11 Aug 2018 - 13:41

178

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Can we turn $\mathbb N_0$ or $\mathbb Z$ into a field?

Published on 25 Mar 2026 - 7:42

243

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what is the multiplicative order of the following elements in $F_{16}$

Published on 11 Aug 2018 - 23:47

104

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Show that $\mathrm{Gal}(E/F)$ is cyclic

Published on 29 Mar 2026 - 8:14

355

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If $F\subset D \subset E$ then $D$ must be a field

Published on 29 Mar 2026 - 6:29

25

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Find $y \in K$, with $K = F(y)$, such that $y^3 \in F$.

Published on 12 Aug 2018 - 8:55

25

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There exist $y \in K$ and $b \in E \setminus F$ such that $\min(y , E) = X^3 - b$ if $\min(z , E) = X^3 - a$ for some $z \in K$ and $a \in E$

Published on 12 Aug 2018 - 9:37

516

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Is $f(z)=2^z$ a homomorphism?

Published on 25 Mar 2026 - 17:38

70

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For which $f \in \mathbb{C}[x,y]$, $\mathbb{C}(x)[y]/(fy-\lambda)$ is isomorphic to $\mathbb{C}(t)$?

Published on 25 Mar 2026 - 17:52

99

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Subfields of $\mathbb{Q}(3^{1/16})$

Published on 29 Mar 2026 - 10:14

2.4k

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Which $f,g \in \mathbb{C}[x,y]$ satisfy $\mathbb{C}(fy,gy)=\mathbb{C}(x,y)$?

Published on 13 Aug 2018 - 8:54

185

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Improper integrals over the reals and surreal numbers

Published on 23 Mar 2026 - 15:27

1k

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Function field in one variable over a finite field.

Published on 29 Mar 2026 - 10:41

597

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How to multiply in the formal Laurent series ring

Published on 26 Mar 2026 - 4:16

54

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Find a chain of fields $F \subseteq E \subseteq K$, where $E \cong F[X]/(X^2 + X + 1)$ and $K \cong E[X]/(X^3 - a)$ for some $a \in E$.

Published on 26 Mar 2026 - 13:02

List Question

In what field do factors of polynomial belong?

Can we turn $\mathbb N_0$ or $\mathbb Z$ into a field?

what is the multiplicative order of the following elements in $F_{16}$

Show that $\mathrm{Gal}(E/F)$ is cyclic

If $F\subset D \subset E$ then $D$ must be a field

Find $y \in K$, with $K = F(y)$, such that $y^3 \in F$.

There exist $y \in K$ and $b \in E \setminus F$ such that $\min(y , E) = X^3 - b$ if $\min(z , E) = X^3 - a$ for some $z \in K$ and $a \in E$

Is $f(z)=2^z$ a homomorphism?

For which $f \in \mathbb{C}[x,y]$, $\mathbb{C}(x)[y]/(fy-\lambda)$ is isomorphic to $\mathbb{C}(t)$?

Subfields of $\mathbb{Q}(3^{1/16})$

Which $f,g \in \mathbb{C}[x,y]$ satisfy $\mathbb{C}(fy,gy)=\mathbb{C}(x,y)$?

Improper integrals over the reals and surreal numbers

Function field in one variable over a finite field.

How to multiply in the formal Laurent series ring

Find a chain of fields $F \subseteq E \subseteq K$, where $E \cong F[X]/(X^2 + X + 1)$ and $K \cong E[X]/(X^3 - a)$ for some $a \in E$.

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