Question

About $\mathbb{Q}(\sqrt{5},\sqrt[3]{7})$

score 55 · Answer 1 · 2026-04-15 20:12:52

55

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About $\mathbb{Q}(\sqrt{5},\sqrt[3]{7})$

Published on 15 Apr 2026 - 20:12

score 11.6k · Answer 2 · 2026-04-15 01:18:19

11.6k

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If $K$ be an algebraic extension of $E$ and $E$ be an algebraic extension of $F$ then $K$ is an algebraic extension of $F$.

Published on 15 Apr 2026 - 1:18

score 1.4k · Answer 3 · 2026-04-14 16:13:32

1.4k

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Prove a Galois group is cyclic

Published on 14 Apr 2026 - 16:13

score 85 · Answer 4 · 2026-04-16 21:50:23

85

Views

$[\mathbb{Q}(\sqrt{2})(\sqrt{6}) : \mathbb{Q}(\sqrt{3})]$ = ?.

Published on 16 Apr 2026 - 21:50

score 176 · Answer 5 · 2026-04-13 00:51:10

176

Views

Corollary of Lifting Lemma for Algebraic Closures

Published on 13 Apr 2026 - 0:51

score 841 · Answer 6 · 2026-03-25 22:25:14

841

Views

Let $d\in \mathbb Q$ , to prove $\mathbb Q(\sqrt d) \subseteq \mathbb Q(e^{2i\pi/n})$ for some positive integer $n$ (without Kronecker-Weber)

Published on 25 Mar 2026 - 22:25

score 234 · Answer 7 · 2026-03-27 11:46:44

234

Views

Finite morphisms over $\operatorname{Spec} O_K$

Published on 27 Mar 2026 - 11:46

score 117 · Answer 8 · 2026-04-15 10:20:53

117

Views

free field extensions vs linearly disjoint field extensions

Published on 15 Apr 2026 - 10:20

score 115 · Answer 9 · 2026-04-09 08:27:53

115

Views

$L/k$ finite extension , $L_1,L_2 $ subfields of $L$ containing $k$ , $L_1/k$ separable and $L_2/k$ normal , then $[L_1L_2:L_2]=[L_1:L_1\cap L_2]$ ?

Published on 09 Apr 2026 - 8:27

score 1.4k · Answer 10 · 2026-04-13 20:20:53

1.4k

Views

Galois group of an irreducible , separable polynomial be abelian , then each of the roots of the polynomial generates the splitting field?

Published on 13 Apr 2026 - 20:20

score 267 · Answer 11 · 2026-03-27 13:42:14

267

Views

$L/k$ finite Galois extension with solvable Galois group divisible by a prime $p$ . Does there exist field $k\subseteq F \subseteq L$ s.t. $p=[F:k]$?

Published on 27 Mar 2026 - 13:42

score 52 · Answer 12 · 2026-04-16 16:49:02

52

Views

If $\mathbb{Q}_p(\sqrt{a}) \cong \mathbb{Q}_p(\sqrt{b})$ ($a,b$ non-squares), then $a/b$ is a square?

Published on 16 Apr 2026 - 16:49

score 139 · Answer 13 · 2026-03-27 15:20:10

139

Views

$\operatorname{char} k=0$, $a,b,c,d,e \in k$ , then is the polynomial $f(x)=ax^8+bx^6+cx^4+dx^2+e$ solvable by radicals over $k$?

Published on 27 Mar 2026 - 15:20

score 484 · Answer 14 · 2026-04-16 12:58:04

If a regular $n$-gon is constructible i.e. if $\cos (2\pi/n)$ is a constructible number then how to show that $\phi(n)$ is a power of $2$?

score 49 · Answer 15 · 2026-03-25 22:30:53

49

Views

$a_n:=e^{2\pi i/n} $ , then how to show that $[\mathbb Q(a_n):\mathbb Q(a_n +1/a_n)]=2$ ?

Published on 25 Mar 2026 - 22:30

List Question

About $\mathbb{Q}(\sqrt{5},\sqrt[3]{7})$

If $K$ be an algebraic extension of $E$ and $E$ be an algebraic extension of $F$ then $K$ is an algebraic extension of $F$.

Prove a Galois group is cyclic

$[\mathbb{Q}(\sqrt{2})(\sqrt{6}) : \mathbb{Q}(\sqrt{3})]$ = ?.

Corollary of Lifting Lemma for Algebraic Closures

Let $d\in \mathbb Q$ , to prove $\mathbb Q(\sqrt d) \subseteq \mathbb Q(e^{2i\pi/n})$ for some positive integer $n$ (without Kronecker-Weber)

Finite morphisms over $\operatorname{Spec} O_K$

free field extensions vs linearly disjoint field extensions

$L/k$ finite extension , $L_1,L_2 $ subfields of $L$ containing $k$ , $L_1/k$ separable and $L_2/k$ normal , then $[L_1L_2:L_2]=[L_1:L_1\cap L_2]$ ?

Galois group of an irreducible , separable polynomial be abelian , then each of the roots of the polynomial generates the splitting field?

$L/k$ finite Galois extension with solvable Galois group divisible by a prime $p$ . Does there exist field $k\subseteq F \subseteq L$ s.t. $p=[F:k]$?

If $\mathbb{Q}_p(\sqrt{a}) \cong \mathbb{Q}_p(\sqrt{b})$ ($a,b$ non-squares), then $a/b$ is a square?

$\operatorname{char} k=0$, $a,b,c,d,e \in k$ , then is the polynomial $f(x)=ax^8+bx^6+cx^4+dx^2+e$ solvable by radicals over $k$?

If a regular $n$-gon is constructible i.e. if $\cos (2\pi/n)$ is a constructible number then how to show that $\phi(n)$ is a power of $2$?

$a_n:=e^{2\pi i/n} $ , then how to show that $[\mathbb Q(a_n):\mathbb Q(a_n +1/a_n)]=2$ ?

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