Question

How to prove that F is extension of K

score 34 · Answer 1 · 2018-04-12 15:24:30

34

Views

How to prove that F is extension of K

Published on 12 Apr 2018 - 15:24

score 29 · Answer 2 · 2018-04-12 17:38:46

29

Views

Do all elements in a quadratic extension of $\mathbb Q$ have degree less than or equal to $2$ over $\mathbb Q$?

Published on 12 Apr 2018 - 17:38

score 268 · Answer 3 · 2018-04-12 21:12:11

268

Views

Determine the quadratic number fields $\mathbb Q[\sqrt{d}]$ that contain a primitive $n$-th root of unity, for some integer $n$.

Published on 12 Apr 2018 - 21:12

score 56 · Answer 4 · 2026-03-25 09:50:11

56

Views

If $w\in\mathbb{Q}(a,b)$, determine $w$ such that $\mathbb{Q}(w)=\mathbb{Q}(a,b)$ with $a,b\in\mathbb{R}$ and are algebraic over $\mathbb{Q}$

Published on 25 Mar 2026 - 9:50

score 675 · Answer 5 · 2018-04-13 10:44:46

675

Views

If F is a field and a,b are in F, c is in an extension field, show that F(ac+b)=F(c)

Published on 13 Apr 2018 - 10:44

score 83 · Answer 6 · 2026-03-25 05:01:11

83

Views

Degree of an extension field

Published on 25 Mar 2026 - 5:01

score 78 · Answer 7 · 2018-04-13 19:43:19

78

Views

$K=F(\alpha)$ if $K$ is a quadratic extension

Published on 13 Apr 2018 - 19:43

score 213 · Answer 8 · 2018-04-13 20:51:11

213

Views

Corollary 15.3.8 from Artin (degrees of field extensions)

Published on 13 Apr 2018 - 20:51

score 2.2k · Answer 9 · 2018-04-14 21:56:58

2.2k

Views

Tower Law and normal field extensions

Published on 14 Apr 2018 - 21:56

score 94 · Answer 10 · 2026-03-23 01:40:27

94

Views

Let $n \geq 3$ and let $p$ be prime. Show that $\sqrt[n]{p}$ is not contained in a cyclotomic extension of $\mathbb{Q}$

Published on 23 Mar 2026 - 1:40

score 594 · Answer 11 · 2026-03-25 11:25:59

594

Views

A question on the definition of splitting field

Published on 25 Mar 2026 - 11:25

score 476 · Answer 12 · 2026-03-17 17:14:59

476

Views

biquadratic extension over a field of characteristic 2

Published on 17 Mar 2026 - 17:14

score 450 · Answer 13 · 2018-04-17 17:46:41

450

Views

How to determine whether the images of two real embeddings of a number field are equal?

Published on 17 Apr 2018 - 17:46

score 1.5k · Answer 14 · 2018-04-17 17:55:33

1.5k

Views

Basis for the field extension $\mathbb{Q}(3^{1/4},i)$ over $\mathbb{Q}$

Published on 17 Apr 2018 - 17:55

score 90 · Answer 15 · 2018-04-17 20:00:18

90

Views

Let $K$ be an extension of $F$. When is $ \operatorname{Aut}(K)= \operatorname{Gal}(K/F)$?

Published on 17 Apr 2018 - 20:00

List Question

How to prove that F is extension of K

Do all elements in a quadratic extension of $\mathbb Q$ have degree less than or equal to $2$ over $\mathbb Q$?

Determine the quadratic number fields $\mathbb Q[\sqrt{d}]$ that contain a primitive $n$-th root of unity, for some integer $n$.

If $w\in\mathbb{Q}(a,b)$, determine $w$ such that $\mathbb{Q}(w)=\mathbb{Q}(a,b)$ with $a,b\in\mathbb{R}$ and are algebraic over $\mathbb{Q}$

If F is a field and a,b are in F, c is in an extension field, show that F(ac+b)=F(c)

Degree of an extension field

$K=F(\alpha)$ if $K$ is a quadratic extension

Corollary 15.3.8 from Artin (degrees of field extensions)

Tower Law and normal field extensions

Let $n \geq 3$ and let $p$ be prime. Show that $\sqrt[n]{p}$ is not contained in a cyclotomic extension of $\mathbb{Q}$

A question on the definition of splitting field

biquadratic extension over a field of characteristic 2

How to determine whether the images of two real embeddings of a number field are equal?

Basis for the field extension $\mathbb{Q}(3^{1/4},i)$ over $\mathbb{Q}$

Let $K$ be an extension of $F$. When is $ \operatorname{Aut}(K)= \operatorname{Gal}(K/F)$?

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