Question

Galois action on $K\otimes_{\mathbb{Q}} \mathbb{Q}_\ell$

score 76 · Answer 1 · 2026-04-16 11:03:32

76

Views

Galois action on $K\otimes_{\mathbb{Q}} \mathbb{Q}_\ell$

Published on 16 Apr 2026 - 11:03

score 636 · Answer 2 · 2026-04-17 09:32:39

636

Views

Let $f(x)= x^3+ax^2+bx+c \in \mathbb{Q}[x]$. Show that the splitting field of $f$ over $\mathbb{Q}$ has degree 1, 2, 3 or 6 over $\mathbb{Q}$.

Published on 17 Apr 2026 - 9:32

score 510 · Answer 3 · 2026-04-16 13:19:07

510

Views

Prove that the Galois group $G = Gal(x^5-2; \mathbb{Q})$ is a group metacyclic.

Published on 16 Apr 2026 - 13:19

score 275 · Answer 4 · 2026-04-12 00:19:58

275

Views

Non cyclic Galois extension of degree 12

Published on 12 Apr 2026 - 0:19

score 153 · Answer 5 · 2026-04-15 09:59:46

153

Views

Norm of a polynomial $N_{E/K}(f)(X)$ with $E/K$ a Galois extension

Published on 15 Apr 2026 - 9:59

score 38 · Answer 6 · 2026-04-14 00:32:04

38

Views

Prove that $\operatorname{Gal}(K_1 / F_1)$ and $\operatorname{Gal}(K_2 / F_2) $ are isomorphic

Published on 14 Apr 2026 - 0:32

score 45 · Answer 7 · 2026-04-16 00:04:06

45

Views

$E=K(a_1,...,a_n)$ and $\sigma \in Gal(E/K)$ such that $\sigma (a_i)=a_i$ for all $i$. Prove $\sigma = 1_E$

Published on 16 Apr 2026 - 0:04

score 67 · Answer 8 · 2026-04-15 03:21:35

67

Views

Is the extension $ℚ(\alpha):ℚ(\alpha^2)$ a Galois extension?

Published on 15 Apr 2026 - 3:21

score 70 · Answer 9 · 2026-04-13 13:33:44

70

Views

Is $(x-t)^p$ irreducible?

Published on 13 Apr 2026 - 13:33

score 121 · Answer 10 · 2026-04-15 02:33:21

121

Views

Splitting field of an infinite family of separable polynomials is infinite dimensional if there is no finite subfamily of which it is splitting.

Published on 15 Apr 2026 - 2:33

score 34 · Answer 11 · 2026-04-15 17:25:23

34

Views

Galois group is dihedral iff $\exists \beta_i\in F$

Published on 15 Apr 2026 - 17:25

score 200 · Answer 12 · 2026-04-09 18:04:49

200

Views

For a recursion based on $x+y+z+2\sqrt{xy+yz+zx},$ does what happens in $\mathbb Z\left[\sqrt n\right]$ stay in $\mathbb Z\left[\sqrt n\right]$?

Published on 09 Apr 2026 - 18:04

score 70 · Answer 13 · 2026-04-16 16:01:31

70

Views

Find the degree of the normal closure $E$ of $F$ over $\mathbb Q$. What is the degree of $E$ over $\mathbb Q$?

Published on 16 Apr 2026 - 16:01

score 530 · Answer 14 · 2026-04-16 05:18:34

530

Views

Solvability by radicals of a separable field of characteristic $p$

Published on 16 Apr 2026 - 5:18

score 151 · Answer 15 · 2026-04-14 13:25:55

151

Views

Possible degrees of an algebraic element in intermediate fields

Published on 14 Apr 2026 - 13:25

List Question

Galois action on $K\otimes_{\mathbb{Q}} \mathbb{Q}_\ell$

Let $f(x)= x^3+ax^2+bx+c \in \mathbb{Q}[x]$. Show that the splitting field of $f$ over $\mathbb{Q}$ has degree 1, 2, 3 or 6 over $\mathbb{Q}$.

Prove that the Galois group $G = Gal(x^5-2; \mathbb{Q})$ is a group metacyclic.

Non cyclic Galois extension of degree 12

Norm of a polynomial $N_{E/K}(f)(X)$ with $E/K$ a Galois extension

Prove that $\operatorname{Gal}(K_1 / F_1)$ and $\operatorname{Gal}(K_2 / F_2) $ are isomorphic

$E=K(a_1,...,a_n)$ and $\sigma \in Gal(E/K)$ such that $\sigma (a_i)=a_i$ for all $i$. Prove $\sigma = 1_E$

Is the extension $ℚ(\alpha):ℚ(\alpha^2)$ a Galois extension?

Is $(x-t)^p$ irreducible?

Splitting field of an infinite family of separable polynomials is infinite dimensional if there is no finite subfamily of which it is splitting.

Galois group is dihedral iff $\exists \beta_i\in F$

For a recursion based on $x+y+z+2\sqrt{xy+yz+zx},$ does what happens in $\mathbb Z\left[\sqrt n\right]$ stay in $\mathbb Z\left[\sqrt n\right]$?

Find the degree of the normal closure $E$ of $F$ over $\mathbb Q$. What is the degree of $E$ over $\mathbb Q$?

Solvability by radicals of a separable field of characteristic $p$

Possible degrees of an algebraic element in intermediate fields

Trending Questions

Popular # Hahtags

Popular Questions