Question

Irreducibility of polynomial $x^n+x+3$ for $n>1$

score 90 · Answer 1 · 2026-03-30 00:05:37

90

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Irreducibility of polynomial $x^n+x+3$ for $n>1$

Published on 30 Mar 2026 - 0:05

score 101 · Answer 2 · 2020-03-27 05:55:05

101

Views

Unable to think about a part of lemma in Chapter Fields and Galois Theory from Algebra by Hungerford

Published on 27 Mar 2020 - 5:55

score 53 · Answer 3 · 2026-04-01 22:21:59

53

Views

Factoring a polynomial over $\mathbb{F}_{101}$.

Published on 01 Apr 2026 - 22:21

score 59 · Answer 4 · 2026-03-28 13:01:36

59

Views

Find an extension $F/L$ such that $F/\mathbb{Q}$ is radical

Published on 28 Mar 2026 - 13:01

score 96 · Answer 5 · 2026-03-26 14:31:59

96

Views

Is $f = X^p - p^2$ irreducible over $\mathbb{Q}$ for $p \geq 3$ a prime number?

Published on 26 Mar 2026 - 14:31

score 85 · Answer 6 · 2026-03-28 12:59:21

85

Views

Galois group of $F/K$ where $F/K$ is galois with $[F:K]=8$ and where there is an intermediate field $E$ with $[E:K]=4$ such that $E/K$ is not galois

Published on 28 Mar 2026 - 12:59

score 175 · Answer 7 · 2020-03-29 18:57:57

175

Views

Find a Galois extension $\mathbb{Q}\subset K$ with $\text{Gal}(K/\mathbb{Q})\cong\mathbb{Z}/3\mathbb{Z}\times\mathbb{Z}/3\mathbb{Z}$

Published on 29 Mar 2020 - 18:57

score 29 · Answer 8 · 2020-03-30 00:34:10

29

Views

Is $\prod (x - (\sqrt[p]{2}\zeta_{p}^s + \sqrt[q]{3}\zeta_{q}^r) )$ a polynomial with rational coefficients, p, q prime?

Published on 30 Mar 2020 - 0:34

score 172 · Answer 9 · 2026-03-26 09:40:02

172

Views

Solving the sextic equation with 14th root of unity

Published on 26 Mar 2026 - 9:40

score 396 · Answer 10 · 2026-03-29 12:05:22

396

Views

Automorphism group of finite field extension has a trivial stabilizer

Published on 29 Mar 2026 - 12:05

score 49 · Answer 11 · 2020-03-30 21:54:47

$\sigma \in$ Gal$(\bar{\mathbb{Q}}/\mathbb{Q})$ induces an isomorphism of local fields $K_v \longrightarrow \sigma(K)_{v^{\sigma}}$ clarification

score 70 · Answer 12 · 2026-03-25 10:58:44

70

Views

Kronecker-Weber à la Wiles

Published on 25 Mar 2026 - 10:58

score 312 · Answer 13 · 2020-03-31 16:39:44

312

Views

Uniqueness of the Frobenius automorphism

Published on 31 Mar 2020 - 16:39

score 54 · Answer 14 · 2026-03-26 16:14:04

54

Views

Let $\omega = e^{\frac{2\pi i}{5}}$. Determine the Galois group $G = Gal(K/\mathbb{Q})$

Published on 26 Mar 2026 - 16:14

score 106 · Answer 15 · 2026-03-28 14:37:49

106

Views

Find the Galois group $Gal(\mathbb{Q}[\sqrt{2}]/\mathbb{Q})$ and determine all intermediate subfields explicitly.

Published on 28 Mar 2026 - 14:37

List Question

Irreducibility of polynomial $x^n+x+3$ for $n>1$

Unable to think about a part of lemma in Chapter Fields and Galois Theory from Algebra by Hungerford

Factoring a polynomial over $\mathbb{F}_{101}$.

Find an extension $F/L$ such that $F/\mathbb{Q}$ is radical

Is $f = X^p - p^2$ irreducible over $\mathbb{Q}$ for $p \geq 3$ a prime number?

Galois group of $F/K$ where $F/K$ is galois with $[F:K]=8$ and where there is an intermediate field $E$ with $[E:K]=4$ such that $E/K$ is not galois

Find a Galois extension $\mathbb{Q}\subset K$ with $\text{Gal}(K/\mathbb{Q})\cong\mathbb{Z}/3\mathbb{Z}\times\mathbb{Z}/3\mathbb{Z}$

Is $\prod (x - (\sqrt[p]{2}\zeta_{p}^s + \sqrt[q]{3}\zeta_{q}^r) )$ a polynomial with rational coefficients, p, q prime?

Solving the sextic equation with 14th root of unity

Automorphism group of finite field extension has a trivial stabilizer

$\sigma \in$ Gal$(\bar{\mathbb{Q}}/\mathbb{Q})$ induces an isomorphism of local fields $K_v \longrightarrow \sigma(K)_{v^{\sigma}}$ clarification

Kronecker-Weber à la Wiles

Uniqueness of the Frobenius automorphism

Let $\omega = e^{\frac{2\pi i}{5}}$. Determine the Galois group $G = Gal(K/\mathbb{Q})$

Find the Galois group $Gal(\mathbb{Q}[\sqrt{2}]/\mathbb{Q})$ and determine all intermediate subfields explicitly.

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