Question

A field such that no extension has an 11th primitive root of unity

score 231 · Answer 1 · 2026-03-27 07:14:45

231

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A field such that no extension has an 11th primitive root of unity

Published on 27 Mar 2026 - 7:14

score 147 · Answer 2 · 2018-05-08 16:03:43

147

Views

Is the unique real root of $X^3-(X+1)$ solvable by real radicals?

Published on 08 May 2018 - 16:03

score 35 · Answer 3 · 2026-03-26 06:32:31

35

Views

Let $r$ and $n$ be integers. Give the Galois correspondance for the extension $F_{p^r} \cap F_{p^n} \leq F_{p^r} \vee F_{p^n}$

Published on 26 Mar 2026 - 6:32

score 35 · Answer 4 · 2018-05-09 14:38:17

35

Views

How to prove $\operatorname{Gal}(L/\mathbb{Q})$ is either $S_3$ or $A_3$

Published on 09 May 2018 - 14:38

score 1.2k · Answer 5 · 2018-05-09 15:34:51

1.2k

Views

How to draw subgroup lattice for extension field $\mathbb{Q}(\sqrt[4]{2},i)$

Published on 09 May 2018 - 15:34

score 88 · Answer 6 · 2018-05-09 19:55:04

88

Views

A question about étale algebras over $\mathbb{Q}$

Published on 09 May 2018 - 19:55

score 282 · Answer 7 · 2026-03-25 20:22:56

282

Views

Let $K$ be a field, Splitting field $L$ over $K$ of polynomial $f(x)=x^n-\theta$

Published on 25 Mar 2026 - 20:22

score 61 · Answer 8 · 2018-05-10 00:58:19

61

Views

Given the splitting field $L$ and a field $K$, Find $Aut(L/K)$

Published on 10 May 2018 - 0:58

score 251 · Answer 9 · 2026-03-25 07:45:30

251

Views

Galois group of symmetric polynomial extension

Published on 25 Mar 2026 - 7:45

score 560 · Answer 10 · 2026-03-26 04:49:29

560

Views

Inseparable elements over $\mathbb F_p(t)$

Published on 26 Mar 2026 - 4:49

score 99 · Answer 11 · 2026-03-22 12:58:08

99

Views

$\mathbb F_p(t) \leq L $ a finite extension

Published on 22 Mar 2026 - 12:58

score 49 · Answer 12 · 2026-03-25 20:22:58

49

Views

Suppose that $f(x)$ has a nonreal root. Show that 2 divides $|\operatorname{Gal}(f(x))|$

Published on 25 Mar 2026 - 20:22

score 39 · Answer 13 · 2018-05-11 02:58:32

39

Views

Let $f(x)$ be irreducible so that $\operatorname{Gal}(f(x)) \simeq Z_{p}$ for p an odd prime. Show that $f(x)$ has degree p and all real zeros.

Published on 11 May 2018 - 2:58

score 59 · Answer 14 · 2026-03-25 20:20:29

59

Views

Let $p$ be a prime that does not divide $m$ and let $\omega$ be a primitive $m$th root of unity over$\mathbb{F}_p$.

Published on 25 Mar 2026 - 20:20

score 91 · Answer 15 · 2026-03-25 13:56:55

91

Views

Show that $\operatorname{Gal}((x^{8}-1)/(x-1))$ is abelian.

Published on 25 Mar 2026 - 13:56

List Question

A field such that no extension has an 11th primitive root of unity

Is the unique real root of $X^3-(X+1)$ solvable by real radicals?

Let $r$ and $n$ be integers. Give the Galois correspondance for the extension $F_{p^r} \cap F_{p^n} \leq F_{p^r} \vee F_{p^n}$

How to prove $\operatorname{Gal}(L/\mathbb{Q})$ is either $S_3$ or $A_3$

How to draw subgroup lattice for extension field $\mathbb{Q}(\sqrt[4]{2},i)$

A question about étale algebras over $\mathbb{Q}$

Let $K$ be a field, Splitting field $L$ over $K$ of polynomial $f(x)=x^n-\theta$

Given the splitting field $L$ and a field $K$, Find $Aut(L/K)$

Galois group of symmetric polynomial extension

Inseparable elements over $\mathbb F_p(t)$

$\mathbb F_p(t) \leq L $ a finite extension

Suppose that $f(x)$ has a nonreal root. Show that 2 divides $|\operatorname{Gal}(f(x))|$

Let $f(x)$ be irreducible so that $\operatorname{Gal}(f(x)) \simeq Z_{p}$ for p an odd prime. Show that $f(x)$ has degree p and all real zeros.

Let $p$ be a prime that does not divide $m$ and let $\omega$ be a primitive $m$th root of unity over$\mathbb{F}_p$.

Show that $\operatorname{Gal}((x^{8}-1)/(x-1))$ is abelian.

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