Question

Galois Group Solution Check

score 55 · Answer 1 · 2026-04-12 10:55:17

55

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Galois Group Solution Check

Published on 12 Apr 2026 - 10:55

score 2.6k · Answer 2 · 2026-04-07 05:53:56

2.6k

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Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$

Published on 07 Apr 2026 - 5:53

score 305 · Answer 3 · 2026-04-13 04:29:24

305

Views

Given the splitting field of a polynomial, how can I show that there are three intermediate extensions which aren't normal?

Published on 13 Apr 2026 - 4:29

score 301 · Answer 4 · 2026-04-13 11:59:09

301

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what is the degree of field extension over base field?

Published on 13 Apr 2026 - 11:59

score 33 · Answer 5 · 2026-04-15 03:23:27

33

Views

Prove that $L_f \vert E$ has degree $2$, or there are exactly three fields satisfying those conditions

Published on 15 Apr 2026 - 3:23

score 315 · Answer 6 · 2026-04-16 17:46:29

315

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I want to show how many intermediate fields there are between $GF(3^{12})$ and $GF(3^4)$.

Published on 16 Apr 2026 - 17:46

score 915 · Answer 7 · 2026-04-14 22:55:38

915

Views

Prove that $\mathbb{Q}$ has extensions of any finite degree in $\mathbb{C}$

Published on 14 Apr 2026 - 22:55

score 110 · Answer 8 · 2026-04-12 12:37:15

110

Views

Explicit automorphisms of the splitting field of a certain quartic over the rationals.

Published on 12 Apr 2026 - 12:37

score 247 · Answer 9 · 2026-04-15 20:49:36

247

Views

$\mathbb{F_2}(\alpha)/\mathbb{F_2}$ is a splitting field of $f(x)$ over $\mathbb{F_2}$

Published on 15 Apr 2026 - 20:49

score 414 · Answer 10 · 2026-04-15 22:51:50

414

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Given $F \subset L \subset K$ where $K$ is a Galois ext. of $F$, find an example where $F \subset L$ is not a Galois ext.

Published on 15 Apr 2026 - 22:51

score 247 · Answer 11 · 2026-04-07 05:53:03

247

Views

Irreducibility Over $\def\Q{\Bbb Q}\Q[\sqrt2]$

Published on 07 Apr 2026 - 5:53

score 677 · Answer 12 · 2026-04-14 20:29:57

677

Views

Degree of field extension $\mathbb{Q}\subseteq\mathbb{Q}(i,i\sqrt2)$

Published on 14 Apr 2026 - 20:29

score 404 · Answer 13 · 2026-04-14 16:48:32

404

Views

Separability and reduced tensor fields

Published on 14 Apr 2026 - 16:48

score 72 · Answer 14 · 2026-03-29 19:09:22

72

Views

Polynomial roots. Finite Extensions.

Published on 29 Mar 2026 - 19:09

score 157 · Answer 15 · 2026-04-16 04:42:29

157

Views

Prove that $K$ is normal over $\mathbb{Q}$ and $K(i)=\mathbb{Q}(i, \sqrt[4]{A})$

Published on 16 Apr 2026 - 4:42

List Question

Galois Group Solution Check

Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$

Given the splitting field of a polynomial, how can I show that there are three intermediate extensions which aren't normal?

what is the degree of field extension over base field?

Prove that $L_f \vert E$ has degree $2$, or there are exactly three fields satisfying those conditions

I want to show how many intermediate fields there are between $GF(3^{12})$ and $GF(3^4)$.

Prove that $\mathbb{Q}$ has extensions of any finite degree in $\mathbb{C}$

Explicit automorphisms of the splitting field of a certain quartic over the rationals.

$\mathbb{F_2}(\alpha)/\mathbb{F_2}$ is a splitting field of $f(x)$ over $\mathbb{F_2}$

Given $F \subset L \subset K$ where $K$ is a Galois ext. of $F$, find an example where $F \subset L$ is not a Galois ext.

Irreducibility Over $\def\Q{\Bbb Q}\Q[\sqrt2]$

Degree of field extension $\mathbb{Q}\subseteq\mathbb{Q}(i,i\sqrt2)$

Separability and reduced tensor fields

Polynomial roots. Finite Extensions.

Prove that $K$ is normal over $\mathbb{Q}$ and $K(i)=\mathbb{Q}(i, \sqrt[4]{A})$

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