Question

Let $\xi=e^{ \frac{2 \pi i}{n}}$, then $x^{n}-1= (x-1)(x- \xi)....(x- \xi^{n-1})$.

score 69 · Answer 1 · 2019-03-06 01:27:43

69

Views

Let $\xi=e^{ \frac{2 \pi i}{n}}$, then $x^{n}-1= (x-1)(x- \xi)....(x- \xi^{n-1})$.

Published on 06 Mar 2019 - 1:27

score 428 · Answer 2 · 2026-03-25 11:04:32

428

Views

How to calculate the Galois group of $x^5+15x+12$?

Published on 25 Mar 2026 - 11:04

score 57 · Answer 3 · 2026-03-31 10:15:35

57

Views

Let $L$ be the splitting field of $x^4+1$ over ℚ. Show that $\mathrm{Aut}_\mathbb Q()$ is $\mathbb Z/2\mathbb Z \times \mathbb Z/2\mathbb Z$

Published on 31 Mar 2026 - 10:15

score 458 · Answer 4 · 2026-03-25 21:01:37

458

Views

Let $f(x)=x^4-x^2-1 \in \Bbb Q[x]$, $K$ is the splitting field of $f$ over $\Bbb Q$.

Published on 25 Mar 2026 - 21:01

score 70 · Answer 5 · 2026-03-30 18:10:02

70

Views

If $f_{K(\alpha)}^{\beta}\big| f_{K}^{\beta}$, then $\deg\left(f_{K(\alpha)}^{\beta}\right)| \deg\left(f_{K}^{\beta}\right)$?

Published on 30 Mar 2026 - 18:10

score 199 · Answer 6 · 2026-03-25 06:06:17

199

Views

Complete valuation, norm of finite extension. Proof of Propositon.

Published on 25 Mar 2026 - 6:06

score 109 · Answer 7 · 2026-03-25 15:43:45

109

Views

Is this polynomial irreducible? $h(x, y) = x^2\ − y^3 \in \mathbb{Q}[x,y]$

Published on 25 Mar 2026 - 15:43

score 561 · Answer 8 · 2026-03-31 12:22:29

561

Views

Polynomials with $S_{p}$ as Galois group over $\mathbb{Q}$?

Published on 31 Mar 2026 - 12:22

score 40 · Answer 9 · 2026-03-31 14:28:21

40

Views

I wonder if $\mathrm{Gal}(E/F) \leq S_{d_1} \times S_{d_2} \times S_{d_3} \times \cdots \times S_{d_n} $ or not

Published on 31 Mar 2026 - 14:28

score 45 · Answer 10 · 2019-03-09 11:06:55

45

Views

Let $z = e^{ \frac {2\pi i}{7}} $ and let $p = z+z^2+z^4 $.Then which of the following options are correct?

Published on 09 Mar 2019 - 11:06

score 667 · Answer 11 · 2026-03-25 22:30:45

667

Views

Did I find the splitting field of $x^3-3x+1$ over $\Bbb Q$?

Published on 25 Mar 2026 - 22:30

score 91 · Answer 12 · 2026-04-01 12:03:39

91

Views

Let $F$ be a field. Is it true that if $[F(\sqrt{D}) : F] = 2$, then $D \in F$?

Published on 01 Apr 2026 - 12:03

score 123 · Answer 13 · 2026-03-25 20:34:07

123

Views

Factor Rings over Finite Fields

Published on 25 Mar 2026 - 20:34

score 336 · Answer 14 · 2019-03-10 12:09:44

336

Views

If $ b \in K $ is algebraic of degree n over $F$ then $ [F (b):F ]=n $. Is the converse true?

Published on 10 Mar 2019 - 12:09

score 89 · Answer 15 · 2026-04-02 10:40:02

89

Views

Two number fields with isomorphic Galois groups but different Galois closure of their maximal real subfields

Published on 02 Apr 2026 - 10:40

List Question

Let $\xi=e^{ \frac{2 \pi i}{n}}$, then $x^{n}-1= (x-1)(x- \xi)....(x- \xi^{n-1})$.

How to calculate the Galois group of $x^5+15x+12$?

Let $L$ be the splitting field of $x^4+1$ over ℚ. Show that $\mathrm{Aut}_\mathbb Q()$ is $\mathbb Z/2\mathbb Z \times \mathbb Z/2\mathbb Z$

Let $f(x)=x^4-x^2-1 \in \Bbb Q[x]$, $K$ is the splitting field of $f$ over $\Bbb Q$.

If $f_{K(\alpha)}^{\beta}\big| f_{K}^{\beta}$, then $\deg\left(f_{K(\alpha)}^{\beta}\right)| \deg\left(f_{K}^{\beta}\right)$?

Complete valuation, norm of finite extension. Proof of Propositon.

Is this polynomial irreducible? $h(x, y) = x^2\ − y^3 \in \mathbb{Q}[x,y]$

Polynomials with $S_{p}$ as Galois group over $\mathbb{Q}$?

I wonder if $\mathrm{Gal}(E/F) \leq S_{d_1} \times S_{d_2} \times S_{d_3} \times \cdots \times S_{d_n} $ or not

Let $z = e^{ \frac {2\pi i}{7}} $ and let $p = z+z^2+z^4 $.Then which of the following options are correct?

Did I find the splitting field of $x^3-3x+1$ over $\Bbb Q$?

Let $F$ be a field. Is it true that if $[F(\sqrt{D}) : F] = 2$, then $D \in F$?

Factor Rings over Finite Fields

If $ b \in K $ is algebraic of degree n over $F$ then $ [F (b):F ]=n $. Is the converse true?

Two number fields with isomorphic Galois groups but different Galois closure of their maximal real subfields

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