Question

How can I compute the discriminant of the field $\mathbb{Q}(\sqrt[3]{28})$?

score 732 · Answer 1 · 2026-03-23 09:25:56

732

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How can I compute the discriminant of the field $\mathbb{Q}(\sqrt[3]{28})$?

Published on 23 Mar 2026 - 9:25

score 144 · Answer 2 · 2018-06-14 20:04:53

144

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Compute $T_{E|\mathbb{Q}}(\alpha)$ and $N_{E|\mathbb{Q}}(\alpha)$ for every $\alpha \in E$.

Published on 14 Jun 2018 - 20:04

score 524 · Answer 3 · 2026-03-24 22:01:26

524

Views

Question about the Cyclotomic polynomial and Cyclotomic field.

Published on 24 Mar 2026 - 22:01

score 53 · Answer 4 · 2018-06-16 04:44:43

53

Views

Proof that $\kappa(A[t])=\kappa(A)(t)$

Published on 16 Jun 2018 - 4:44

score 282 · Answer 5 · 2018-06-17 02:06:57

282

Views

Fundamental Theorem of Galois Theory and correspondence between fields and subgroups.

Published on 17 Jun 2018 - 2:06

score 206 · Answer 6 · 2026-03-27 04:04:48

206

Views

Pullback of the Frobenius map and function fields extension

Published on 27 Mar 2026 - 4:04

score 363 · Answer 7 · 2018-06-17 21:27:00

363

Views

If $f(x) \in \mathbb{Q}[x]$ is a monic irreducible polynomial of degree $3$, then $f$ has no roots in $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$.

Published on 17 Jun 2018 - 21:27

score 150 · Answer 8 · 2018-06-17 21:49:55

150

Views

$|\mathbb{Q}(a):\mathbb{Q}|=n,|\mathbb{Q}(b):\mathbb{Q}| =m$ and $\gcd(m,n)=1 \implies|\mathbb{Q}(ab):\mathbb{Q}|=mn$

Published on 17 Jun 2018 - 21:49

score 269 · Answer 9 · 2018-06-20 01:45:21

269

Views

How to compute the degree of $\mathbb{Q}[\sqrt[3]{2}+\sqrt[5]{2}]$ over $\mathbb{Q}$?

Published on 20 Jun 2018 - 1:45

score 168 · Answer 10 · 2018-06-22 18:20:42

168

Views

If an extension is locally Galois, is it Galois?

Published on 22 Jun 2018 - 18:20

score 1.4k · Answer 11 · 2026-03-25 05:41:29

1.4k

Views

Primitive $p$-th root of unity with characteristic $p$

Published on 25 Mar 2026 - 5:41

score 91 · Answer 12 · 2018-06-23 05:09:45

91

Views

How I can show that $\sqrt[3]{x}$ is separable over $\mathbb{Z}_{2}(x)$?

Published on 23 Jun 2018 - 5:09

score 161 · Answer 13 · 2018-06-23 14:03:17

161

Views

Is there an algebraic extension $K / \Bbb Q$ such that $\text{Aut}_{\Bbb Q}(K) \cong \Bbb Z$?

Published on 23 Jun 2018 - 14:03

score 130 · Answer 14 · 2018-06-24 15:44:54

130

Views

Field having exactly two extensions of each degree

Published on 24 Jun 2018 - 15:44

score 67 · Answer 15 · 2018-06-24 15:51:54

67

Views

Fundamental Theorem of Galois Theory and cyclic group of order $30$ (Proof verification)

Published on 24 Jun 2018 - 15:51

List Question

How can I compute the discriminant of the field $\mathbb{Q}(\sqrt[3]{28})$?

Compute $T_{E|\mathbb{Q}}(\alpha)$ and $N_{E|\mathbb{Q}}(\alpha)$ for every $\alpha \in E$.

Question about the Cyclotomic polynomial and Cyclotomic field.

Proof that $\kappa(A[t])=\kappa(A)(t)$

Fundamental Theorem of Galois Theory and correspondence between fields and subgroups.

Pullback of the Frobenius map and function fields extension

If $f(x) \in \mathbb{Q}[x]$ is a monic irreducible polynomial of degree $3$, then $f$ has no roots in $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$.

$|\mathbb{Q}(a):\mathbb{Q}|=n,|\mathbb{Q}(b):\mathbb{Q}| =m$ and $\gcd(m,n)=1 \implies|\mathbb{Q}(ab):\mathbb{Q}|=mn$

How to compute the degree of $\mathbb{Q}[\sqrt[3]{2}+\sqrt[5]{2}]$ over $\mathbb{Q}$?

If an extension is locally Galois, is it Galois?

Primitive $p$-th root of unity with characteristic $p$

How I can show that $\sqrt[3]{x}$ is separable over $\mathbb{Z}_{2}(x)$?

Is there an algebraic extension $K / \Bbb Q$ such that $\text{Aut}_{\Bbb Q}(K) \cong \Bbb Z$?

Field having exactly two extensions of each degree

Fundamental Theorem of Galois Theory and cyclic group of order $30$ (Proof verification)

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