List questions from field-theory

Published on 15 Apr 2026 - 20:43

38

Views

Proper geometrically integral scheme $X$ over $k$ has $k$ as subfield $\mathcal{O}_X(U)$?

Published on 13 Apr 2026 - 8:08

103

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$f = X^{3} + 2$ irreducible in $\mathbb{F}_{49}[X]$.

Published on 17 Apr 2026 - 4:38

24

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Main idea of the proof of the Galois solvability criterion

Published on 13 Apr 2026 - 14:08

38

Views

Minimal polynomial of all elements in a finite field extension of $\mathbb{F}_3$.

Published on 16 Apr 2026 - 2:10

45

Views

Definition of roots of a polynomial

Published on 12 Apr 2026 - 12:13

183

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What is the motivation for building the hyperreals using an ultrapower construction?

Published on 09 Apr 2026 - 21:16

64

Views

Every subring of a field is an integral domain

Published on 10 Apr 2026 - 5:05

40

Views

On the complexity of global fields isomorphism

Published on 11 May 2026 - 7:33

42

Views

If $K$ is a field of characteristic $0$ in which every polynomial of degree $\geq3$ is reducible, then $\bar{K}/K$ has degree $1$ or $2$

Published on 16 Apr 2026 - 2:30

103

Views

Irreducible $p(x) \in \mathbb{Q}[X]$ with roots $r, s$ such that $rs = 1$.

Published on 16 Apr 2026 - 8:41

47

Views

Reducing an inseparable polynomial over the same field to a separable polynomial over a field

Published on 11 Apr 2026 - 11:10

28

Views

Equivalent definition of a perfect field

Published on 11 Apr 2026 - 11:03

39

Views

Prove that $\mathbb F_{p^m} \subseteq \mathbb F_{p^n}$ iff $m$ divides $n$

Published on 16 Apr 2026 - 18:52

77

Views

Arguments for Galois closure of $\mathbb{Q}(\sqrt[3]{2})$

Published on 16 Apr 2026 - 5:33

List Question

Roots of $x^2-x+2=0 \in \mathbb{Z}_3[i]$

Proper geometrically integral scheme $X$ over $k$ has $k$ as subfield $\mathcal{O}_X(U)$?

$f = X^{3} + 2$ irreducible in $\mathbb{F}_{49}[X]$.

Main idea of the proof of the Galois solvability criterion

Minimal polynomial of all elements in a finite field extension of $\mathbb{F}_3$.

Definition of roots of a polynomial

What is the motivation for building the hyperreals using an ultrapower construction?

Every subring of a field is an integral domain

On the complexity of global fields isomorphism

If $K$ is a field of characteristic $0$ in which every polynomial of degree $\geq3$ is reducible, then $\bar{K}/K$ has degree $1$ or $2$

Irreducible $p(x) \in \mathbb{Q}[X]$ with roots $r, s$ such that $rs = 1$.

Reducing an inseparable polynomial over the same field to a separable polynomial over a field

Equivalent definition of a perfect field

Prove that $\mathbb F_{p^m} \subseteq \mathbb F_{p^n}$ iff $m$ divides $n$

Arguments for Galois closure of $\mathbb{Q}(\sqrt[3]{2})$

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