Question

A field extension of degree $\leq 2$

score 95 · Answer 1 · 2026-03-21 13:11:12

95

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A field extension of degree $\leq 2$

Published on 21 Mar 2026 - 13:11

score 278 · Answer 2 · 2026-03-19 15:32:28

278

Views

Eigenvalues of an element in a field extension

Published on 19 Mar 2026 - 15:32

score 124 · Answer 3 · 2026-03-20 06:22:56

124

Views

ch.1 proposition 14 in Lang's Algebraic Number Theory

Published on 20 Mar 2026 - 6:22

score 416 · Answer 4 · 2026-03-23 04:44:08

416

Views

Infinite Cyclotomic Extension of $\mathbb{Q}$

Published on 23 Mar 2026 - 4:44

score 86 · Answer 5 · 2026-03-19 17:53:36

86

Views

How to write cyclotomic field extensions $\mathbb{Q}(\zeta_n)$ in terms of roots and $i$?

Published on 19 Mar 2026 - 17:53

score 197 · Answer 6 · 2026-03-24 20:46:40

197

Views

$f\in K[X]$ irreducible odd degree, $\alpha, \beta\in\bar K$ distinct roots of $f$ $\Rightarrow$ neither $\alpha+\beta\in K$ nor $\alpha\beta\in K$

Published on 24 Mar 2026 - 20:46

score 215 · Answer 7 · 2026-03-24 22:01:20

215

Views

Prove that $\mathbb{Q}[\sqrt[4](7), i] = \mathbb{Q}[\sqrt[4](7)+ i]$

Published on 24 Mar 2026 - 22:01

score 66 · Answer 8 · 2026-03-26 09:19:52

66

Views

Finding an automorphism of $\mathbb{C}(x,y)$ that fixes two given elements

Published on 26 Mar 2026 - 9:19

score 173 · Answer 9 · 2026-03-26 09:15:03

173

Views

Minimal polynomial are same for $\lambda$ and $\lambda ^2$

Published on 26 Mar 2026 - 9:15

score 39 · Answer 10 · 2018-01-23 19:19:35

39

Views

Expressing eigenvalues of a symmetric matrix in terms of its entries

Published on 23 Jan 2018 - 19:19

score 230 · Answer 11 · 2026-03-20 07:00:31

230

Views

How is $\operatorname{Gal}(K^{nr}/K)$ isomorphic to $\operatorname{Gal}(\bar{k}/k)$?

Published on 20 Mar 2026 - 7:00

score 1.2k · Answer 12 · 2026-03-23 02:01:26

1.2k

Views

Criteria for a cubic polynomial in $\Bbb Q[x]$ to split completely over $\Bbb Q_p$

Published on 23 Mar 2026 - 2:01

score 316 · Answer 13 · 2018-01-24 14:05:25

316

Views

What elements of the field extension are fixed by the subgroup $\mathbb Z_3$

Published on 24 Jan 2018 - 14:05

score 87 · Answer 14 · 2026-03-25 01:18:51

87

Views

Finding the Galois group of $\mathbb{Q}(\alpha,i)|\mathbb{Q}$, whereby $\alpha^2 = \frac{3}{2}+\frac{1}{2}i\sqrt7$

Published on 25 Mar 2026 - 1:18

score 90 · Answer 15 · 2026-03-20 06:37:01

90

Views

How to find $\operatorname{Gal}(S/\mathbb{Q})$

Published on 20 Mar 2026 - 6:37

List Question

A field extension of degree $\leq 2$

Eigenvalues of an element in a field extension

ch.1 proposition 14 in Lang's Algebraic Number Theory

Infinite Cyclotomic Extension of $\mathbb{Q}$

How to write cyclotomic field extensions $\mathbb{Q}(\zeta_n)$ in terms of roots and $i$?

$f\in K[X]$ irreducible odd degree, $\alpha, \beta\in\bar K$ distinct roots of $f$ $\Rightarrow$ neither $\alpha+\beta\in K$ nor $\alpha\beta\in K$

Prove that $\mathbb{Q}[\sqrt[4](7), i] = \mathbb{Q}[\sqrt[4](7)+ i]$

Finding an automorphism of $\mathbb{C}(x,y)$ that fixes two given elements

Minimal polynomial are same for $\lambda$ and $\lambda ^2$

Expressing eigenvalues of a symmetric matrix in terms of its entries

How is $\operatorname{Gal}(K^{nr}/K)$ isomorphic to $\operatorname{Gal}(\bar{k}/k)$?

Criteria for a cubic polynomial in $\Bbb Q[x]$ to split completely over $\Bbb Q_p$

What elements of the field extension are fixed by the subgroup $\mathbb Z_3$

Finding the Galois group of $\mathbb{Q}(\alpha,i)|\mathbb{Q}$, whereby $\alpha^2 = \frac{3}{2}+\frac{1}{2}i\sqrt7$

How to find $\operatorname{Gal}(S/\mathbb{Q})$

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