List questions from field-theory

Published on 11 May 2026 - 7:33

52

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$x^2+3$ has two zeros over ${\Bbb F}_p$ provided that $x^2+x+1\in{\Bbb F}_p[x]$ has two?

Published on 16 Apr 2026 - 20:20

53

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Why is $\sqrt{5}$ an element of every field of order $p^{2 e}$?

Published on 15 Apr 2026 - 6:10

285

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Primitive element and field extension

Published on 13 Apr 2026 - 17:09

41

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$K-$rational solution of the equation - Is $\mathbb{Q} \leq \mathbb{Q}_p$?

Published on 16 Apr 2026 - 5:50

51

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The most general splitting of a field extension

Published on 14 Apr 2026 - 11:55

2.3k

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Converse of the theorem "If a real number $c$ is constructible, then $c$ is algebraic of degree a power of 2 over the field $\mathbb{Q}$ of rationals"

Published on 15 Apr 2026 - 12:31

3.9k

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Cyclotomic polynomials and Galois group

Published on 13 Apr 2026 - 12:34

227

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Spaces vs. Structures

Published on 09 Apr 2026 - 13:43

898

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Cyclotomic polynomials and Galois groups

Published on 12 Apr 2026 - 13:55

29

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Evaluating minimal polynomial over a field $F$ as a characteristic polynomial for a $F$-linear map.

Published on 13 Apr 2026 - 16:45

131

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Which algebraic intuition can be used in fields

Published on 11 Apr 2026 - 13:08

279

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Find the irreducible polynomial of $\zeta_{12}$ and $\zeta_9$ over the field $Q(\zeta_3)$.

Published on 16 Apr 2026 - 4:37

700

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Prove or disprove that Q[√2] is a field

Published on 16 Apr 2026 - 15:59

221

Views

extension field homomorphisms

Published on 12 Apr 2026 - 6:56

List Question

computing the full constant field of an algebraic function field

$x^2+3$ has two zeros over ${\Bbb F}_p$ provided that $x^2+x+1\in{\Bbb F}_p[x]$ has two?

Why is $\sqrt{5}$ an element of every field of order $p^{2 e}$?

Primitive element and field extension

$K-$rational solution of the equation - Is $\mathbb{Q} \leq \mathbb{Q}_p$?

The most general splitting of a field extension

Converse of the theorem "If a real number $c$ is constructible, then $c$ is algebraic of degree a power of 2 over the field $\mathbb{Q}$ of rationals"

Cyclotomic polynomials and Galois group

Spaces vs. Structures

Cyclotomic polynomials and Galois groups

Evaluating minimal polynomial over a field $F$ as a characteristic polynomial for a $F$-linear map.

Which algebraic intuition can be used in fields

Find the irreducible polynomial of $\zeta_{12}$ and $\zeta_9$ over the field $Q(\zeta_3)$.

Prove or disprove that Q[√2] is a field

extension field homomorphisms

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