List questions from field-theory

Published on 16 Apr 2026 - 9:04

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Analytic equivalence and isomorphism of valued fields

Published on 13 Apr 2026 - 11:36

52

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Is this extension cyclic? proof of Dummit and Foote

Published on 12 Apr 2026 - 0:58

64

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$E := \mathbb{Q}( \sqrt{3}, \sqrt{5}, \sqrt[3]{7})/ \mathbb{Q}$. Determine a $ϑ ∈ E$ with $E = \mathbb{Q}(ϑ)$.

Published on 17 Apr 2026 - 16:02

85

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If $\alpha^3-\alpha+1=0$ then $\sqrt{3}\neq a\alpha^2+b\alpha+c$ for $a$, $b$, $c\in \mathbf{Q}$

Published on 17 Apr 2026 - 14:07

70

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An exercise where I need to prove that a field extension is normal

Published on 14 Apr 2026 - 6:25

89

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$K$-automorphisms permuting the roots of $f$ in $L$.

Published on 14 Apr 2026 - 12:23

30

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Why must the order of a finite field be the power of a prime?

Published on 16 Apr 2026 - 13:36

64

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What are the proper subfields of the cyclotomic field extension generated by a primitive fifth root of unity?

Published on 25 Mar 2026 - 19:25

110

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Finding the minimal monic polynomial given a root

Published on 10 Apr 2026 - 19:16

62

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Computing the Galois group of polynomials of high degree

Published on 11 Apr 2026 - 21:58

76

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Examples of mathematical Fields that don't revolve around numbers?

Published on 16 Apr 2026 - 5:19

89

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Show $x^5+x^4+x^2+x+1$ is irreducible in $\mathbb{Q}(\sqrt[5]{2})$

Published on 16 Apr 2026 - 19:10

103

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Integration by substitution, but from sphere to sphere

Published on 07 Apr 2026 - 21:18

62

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Number of Linear Factors of $x^{\frac{p-1}{2}}-1$ in $\mathbb{Z}_p$

Published on 13 Apr 2026 - 21:08

List Question

Show quotient ring and matrix ring are isomorphic

Analytic equivalence and isomorphism of valued fields

Is this extension cyclic? proof of Dummit and Foote

$E := \mathbb{Q}( \sqrt{3}, \sqrt{5}, \sqrt[3]{7})/ \mathbb{Q}$. Determine a $ϑ ∈ E$ with $E = \mathbb{Q}(ϑ)$.

If $\alpha^3-\alpha+1=0$ then $\sqrt{3}\neq a\alpha^2+b\alpha+c$ for $a$, $b$, $c\in \mathbf{Q}$

An exercise where I need to prove that a field extension is normal

$K$-automorphisms permuting the roots of $f$ in $L$.

Why must the order of a finite field be the power of a prime?

What are the proper subfields of the cyclotomic field extension generated by a primitive fifth root of unity?

Finding the minimal monic polynomial given a root

Computing the Galois group of polynomials of high degree

Examples of mathematical Fields that don't revolve around numbers?

Show $x^5+x^4+x^2+x+1$ is irreducible in $\mathbb{Q}(\sqrt[5]{2})$

Integration by substitution, but from sphere to sphere

Number of Linear Factors of $x^{\frac{p-1}{2}}-1$ in $\mathbb{Z}_p$

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