Question

algebraic closure of an algebraically closed field is itself?

score 137 · Answer 1 · 2018-11-11 14:49:10

137

Views

algebraic closure of an algebraically closed field is itself?

Published on 11 Nov 2018 - 14:49

score 388 · Answer 2 · 2026-03-26 13:01:20

388

Views

Decomposition field of $x^n - 1$ over $Z_p$

Published on 26 Mar 2026 - 13:01

score 68 · Answer 3 · 2018-11-12 02:05:45

68

Views

Degree of field extensions $\mathbb Q(\alpha)/\mathbb Q$ and $\mathbb Q(\alpha^{12})/\mathbb Q$, where $\alpha = 2^{1/3}+3^{1/4}$

Published on 12 Nov 2018 - 2:05

score 547 · Answer 4 · 2026-03-25 16:01:47

547

Views

minimal polynomial of $\sin (2\pi/7)$ over $\mathbb Q(\sqrt 7)$

Published on 25 Mar 2026 - 16:01

score 177 · Answer 5 · 2018-11-12 11:15:45

177

Views

Does $i$ belong to $\Bbb Q(\sqrt[4]{-p})$?

Published on 12 Nov 2018 - 11:15

score 153 · Answer 6 · 2026-02-23 01:18:54

153

Views

Show that $\mathbb{Q}[\sqrt{2},\sqrt{3}] $ is separable

Published on 23 Feb 2026 - 1:18

score 160 · Answer 7 · 2018-11-13 07:37:54

160

Views

If $E/F$ is a finite extension and $E = F(\alpha)$ for some $\alpha\in E,$ is it true that $E/F$ separable?

Published on 13 Nov 2018 - 7:37

score 368 · Answer 8 · 2026-03-23 12:50:18

368

Views

"Purely inseparable, algebraic extension if and only if trivial automorphism group"

Published on 23 Mar 2026 - 12:50

score 49 · Answer 9 · 2026-02-23 01:22:13

49

Views

Sum of algebraic number of prime degree.

Published on 23 Feb 2026 - 1:22

score 66 · Answer 10 · 2018-11-15 19:57:36

66

Views

Identifying squares in field extension

Published on 15 Nov 2018 - 19:57

score 71 · Answer 11 · 2026-03-26 14:34:32

71

Views

Intermediary Extensions of $\mathbb{K}=\mathbb{Q}(\frac{\sqrt{2}}{2}+i\frac{\sqrt{2}}{2})$.

Published on 26 Mar 2026 - 14:34

score 253 · Answer 12 · 2018-11-17 07:23:52

253

Views

Artin-Schreier Extensions

Published on 17 Nov 2018 - 7:23

score 1.3k · Answer 13 · 2026-03-25 17:26:01

1.3k

Views

Size of $\mathrm{Gal}(\mathbb{Q}(\cos(2\pi/7))/\mathbb{Q})$

Published on 25 Mar 2026 - 17:26

score 25 · Answer 14 · 2018-11-17 22:53:29

25

Views

How to show the existence of $\alpha_1,\cdots,\alpha_n$ as a basis of $L|K$ which is contained in $B$?

Published on 17 Nov 2018 - 22:53

score 412 · Answer 15 · 2018-11-19 13:59:04

412

Views

All $\mathbb{Q}$-automorphism of $\mathbb{Q}(\sqrt{3},\sqrt{5})$

Published on 19 Nov 2018 - 13:59

List Question

algebraic closure of an algebraically closed field is itself?

Decomposition field of $x^n - 1$ over $Z_p$

Degree of field extensions $\mathbb Q(\alpha)/\mathbb Q$ and $\mathbb Q(\alpha^{12})/\mathbb Q$, where $\alpha = 2^{1/3}+3^{1/4}$

minimal polynomial of $\sin (2\pi/7)$ over $\mathbb Q(\sqrt 7)$

Does $i$ belong to $\Bbb Q(\sqrt[4]{-p})$?

Show that $\mathbb{Q}[\sqrt{2},\sqrt{3}] $ is separable

If $E/F$ is a finite extension and $E = F(\alpha)$ for some $\alpha\in E,$ is it true that $E/F$ separable?

"Purely inseparable, algebraic extension if and only if trivial automorphism group"

Sum of algebraic number of prime degree.

Identifying squares in field extension

Intermediary Extensions of $\mathbb{K}=\mathbb{Q}(\frac{\sqrt{2}}{2}+i\frac{\sqrt{2}}{2})$.

Artin-Schreier Extensions

Size of $\mathrm{Gal}(\mathbb{Q}(\cos(2\pi/7))/\mathbb{Q})$

How to show the existence of $\alpha_1,\cdots,\alpha_n$ as a basis of $L|K$ which is contained in $B$?

All $\mathbb{Q}$-automorphism of $\mathbb{Q}(\sqrt{3},\sqrt{5})$

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