Question

How to prove that F is extension of K

score 37 · Answer 1 · 2026-04-10 23:52:31

37

Views

How to prove that F is extension of K

Published on 10 Apr 2026 - 23:52

score 31 · Answer 2 · 2026-04-15 06:56:14

31

Views

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

Published on 15 Apr 2026 - 6:56

score 271 · Answer 3 · 2026-04-15 13:57:57

271

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 15 Apr 2026 - 13:57

score 59 · Answer 4 · 2026-05-10 14:07:27

59

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 10 May 2026 - 14:07

score 678 · Answer 5 · 2026-04-17 05:59:20

678

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 17 Apr 2026 - 5:59

score 87 · Answer 6 · 2026-05-11 04:36:10

87

Views

Degree of an extension field

Published on 11 May 2026 - 4:36

score 81 · Answer 7 · 2026-04-15 17:23:47

81

Views

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

Published on 15 Apr 2026 - 17:23

score 216 · Answer 8 · 2026-04-16 03:55:25

216

Views

Corollary 15.3.8 from Artin (degrees of field extensions)

Published on 16 Apr 2026 - 3:55

score 2.2k · Answer 9 · 2026-04-13 16:54:15

2.2k

Views

Tower Law and normal field extensions

Published on 13 Apr 2026 - 16:54

score 101 · Answer 10 · 2026-05-11 00:27:14

101

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 11 May 2026 - 0:27

score 598 · Answer 11 · 2026-05-10 15:18:52

598

Views

A question on the definition of splitting field

Published on 10 May 2026 - 15:18

score 479 · Answer 12 · 2026-04-14 16:59:01

479

Views

biquadratic extension over a field of characteristic 2

Published on 14 Apr 2026 - 16:59

score 453 · Answer 13 · 2026-04-15 09:00:13

453

Views

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

Published on 15 Apr 2026 - 9:00

score 1.5k · Answer 14 · 2026-04-16 02:37:20

1.5k

Views

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

Published on 16 Apr 2026 - 2:37

score 93 · Answer 15 · 2026-04-16 15:23:03

93

Views

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

Published on 16 Apr 2026 - 15:23

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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