List questions from field-theory

Published on 31 Mar 2026 - 23:49

31

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Does the $\mathrm{Spec}(F)$ equal $\overline{F}$ for a field $F$?

Published on 31 Mar 2026 - 23:50

147

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$F$ is algebraically closed $\iff$ $\nexists$ $K$ s.t. $F \leq K$, $K \neq F$ and $[K:F] < \infty$

Published on 23 Jun 2019 - 19:33

216

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Intersection of completion of subextension with algebraic closure

Published on 25 Mar 2026 - 10:55

194

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Minimal polynomial of an element of the field extension $L/ \mathbb{F}_2$.

Published on 31 Mar 2026 - 23:54

158

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Order of a finite multiplicative subgroup of a field

Published on 26 Jun 2019 - 9:00

184

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exercise about some field extensions

Published on 01 Apr 2026 - 21:07

222

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For $\alpha = \sqrt[3]{2} + i$, find the minimal polynomial over $\mathbb{Q}$ and over $\mathbb{Q}[\sqrt[3]{2}]$

Published on 27 Mar 2026 - 5:39

85

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Name for operators that preserve structure?

Published on 27 Jun 2019 - 17:48

166

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Intuition on embeddings, regulator, discriminant of number fields.

Published on 27 Jun 2019 - 22:25

612

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Show that $\mathbb{Q}[\sqrt{7}]$ is a field of fractions of $\mathbb{Z}[\sqrt{7}]$

Published on 27 Jun 2019 - 22:39

356

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Using the field axioms of real numbers, prove that $y=\frac{1}{x}$ if $xy = 1$ and $x ≠ 0$.

Published on 26 Mar 2026 - 9:34

169

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Structure of $F=\mathbb Q(\sqrt {2i})$?

Published on 04 Apr 2026 - 1:57

36

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Theta function of an ideal

Published on 26 Mar 2026 - 21:28

56

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Which one is Field

Published on 29 Jun 2019 - 10:09

List Question

Finding $[\mathbb{Q}(\sqrt{3}, i\sqrt{2}):\mathbb{Q}(\sqrt{3})]$

Does the $\mathrm{Spec}(F)$ equal $\overline{F}$ for a field $F$?

$F$ is algebraically closed $\iff$ $\nexists$ $K$ s.t. $F \leq K$, $K \neq F$ and $[K:F] < \infty$

Intersection of completion of subextension with algebraic closure

Minimal polynomial of an element of the field extension $L/ \mathbb{F}_2$.

Order of a finite multiplicative subgroup of a field

exercise about some field extensions

For $\alpha = \sqrt[3]{2} + i$, find the minimal polynomial over $\mathbb{Q}$ and over $\mathbb{Q}[\sqrt[3]{2}]$

Name for operators that preserve structure?

Intuition on embeddings, regulator, discriminant of number fields.

Show that $\mathbb{Q}[\sqrt{7}]$ is a field of fractions of $\mathbb{Z}[\sqrt{7}]$

Using the field axioms of real numbers, prove that $y=\frac{1}{x}$ if $xy = 1$ and $x ≠ 0$.

Structure of $F=\mathbb Q(\sqrt {2i})$?

Theta function of an ideal

Which one is Field

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