Question

What is the relationship between Gal($K_1/F_1$) and Gal$(K_2/F_2)$?

score 203 · Answer 1 · 2018-05-24 17:01:53

203

Views

What is the relationship between Gal($K_1/F_1$) and Gal$(K_2/F_2)$?

Published on 24 May 2018 - 17:01

score 276 · Answer 2 · 2026-03-25 05:41:31

276

Views

degree of extension of Q with primitive roots of unity

Published on 25 Mar 2026 - 5:41

score 168 · Answer 3 · 2018-05-24 21:21:27

168

Views

$f=x^4+1$ is reducible over infinite field $F$ with characteristic $p>0$

Published on 24 May 2018 - 21:21

score 40 · Answer 4 · 2018-05-26 21:00:46

40

Views

Calculating Galois groups of Quartics

Published on 26 May 2018 - 21:00

score 325 · Answer 5 · 2018-05-28 03:52:20

325

Views

How to think about transcendental field extensions?

Published on 28 May 2018 - 3:52

score 93 · Answer 6 · 2018-05-29 11:41:03

93

Views

$F=\mathbb{Q}(\alpha_1,\alpha_2, ... , \alpha_n)$, where $\alpha_i^2 \in \mathbb{Q}$ implies $\sqrt[3]{2} \notin F$

Published on 29 May 2018 - 11:41

score 102 · Answer 7 · 2018-05-30 13:55:54

102

Views

Cyclotomic field of $\mathbb{Q}(\zeta)$

Published on 30 May 2018 - 13:55

score 193 · Answer 8 · 2018-05-30 17:33:40

193

Views

a basis for the simple extension $F(\alpha)$ over $F$

Published on 30 May 2018 - 17:33

score 1.1k · Answer 9 · 2018-05-31 11:21:18

1.1k

Views

Minimal polynomial of $\sqrt{\sqrt[3]{7}-5}$

Published on 31 May 2018 - 11:21

score 664 · Answer 10 · 2026-03-23 13:00:19

664

Views

If $L/K$ normal and $H = \operatorname{Aut}(L/K)$, then $L/L^H$ is separable and $L^H/K$ is purely inseparable.

Published on 23 Mar 2026 - 13:00

score 180 · Answer 11 · 2018-06-01 15:35:11

180

Views

Vakil 11.2.A: Transitivity of an equivalence relation involving composita of fields

Published on 01 Jun 2018 - 15:35

score 22 · Answer 12 · 2018-06-01 21:22:33

22

Views

The sum of two algebraic points is a new algebraic point

Published on 01 Jun 2018 - 21:22

score 1.1k · Answer 13 · 2026-02-23 01:22:38

1.1k

Views

Let $L:K$ be a Galois extention, show that $L:M$ is a normal.

Published on 23 Feb 2026 - 1:22

score 433 · Answer 14 · 2018-06-04 17:13:10

433

Views

Is a proper ideal of a polynomial ring (on a field) still proper in the polynomial ring on a field extension?

Published on 04 Jun 2018 - 17:13

score 221 · Answer 15 · 2018-06-05 17:56:37

221

Views

Algebraic Torus: Etymology

Published on 05 Jun 2018 - 17:56

List Question

What is the relationship between Gal($K_1/F_1$) and Gal$(K_2/F_2)$?

degree of extension of Q with primitive roots of unity

$f=x^4+1$ is reducible over infinite field $F$ with characteristic $p>0$

Calculating Galois groups of Quartics

How to think about transcendental field extensions?

$F=\mathbb{Q}(\alpha_1,\alpha_2, ... , \alpha_n)$, where $\alpha_i^2 \in \mathbb{Q}$ implies $\sqrt[3]{2} \notin F$

Cyclotomic field of $\mathbb{Q}(\zeta)$

a basis for the simple extension $F(\alpha)$ over $F$

Minimal polynomial of $\sqrt{\sqrt[3]{7}-5}$

If $L/K$ normal and $H = \operatorname{Aut}(L/K)$, then $L/L^H$ is separable and $L^H/K$ is purely inseparable.

Vakil 11.2.A: Transitivity of an equivalence relation involving composita of fields

The sum of two algebraic points is a new algebraic point

Let $L:K$ be a Galois extention, show that $L:M$ is a normal.

Is a proper ideal of a polynomial ring (on a field) still proper in the polynomial ring on a field extension?

Algebraic Torus: Etymology

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