Question

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

score 103 · Answer 1 · 2026-03-28 08:37:14

103

Views

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

Published on 28 Mar 2026 - 8:37

score 198 · Answer 2 · 2026-03-26 09:38:21

198

Views

Constructing composite Galois field with arbitrary primitive polynomial?

Published on 26 Mar 2026 - 9:38

score 194 · Answer 3 · 2026-03-28 08:30:34

194

Views

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

Published on 28 Mar 2026 - 8:30

score 183 · Answer 4 · 2026-03-22 16:29:33

183

Views

Show that this Galois group is solvable (Base case)

Published on 22 Mar 2026 - 16:29

score 109 · Answer 5 · 2026-03-28 19:30:54

109

Views

Prove this homomorphism gives an equivalent definition of Linear Space

Published on 28 Mar 2026 - 19:30

score 280 · Answer 6 · 2018-05-31 01:12:23

280

Views

How to solve a system of equations in a field

Published on 31 May 2018 - 1:12

score 1.1k · Answer 7 · 2026-03-28 12:03:39

1.1k

Views

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

Published on 28 Mar 2026 - 12:03

score 664 · Answer 8 · 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 299 · Answer 9 · 2026-03-25 11:13:26

299

Views

Galois group of the general (indeterminate) polynomial equation

Published on 25 Mar 2026 - 11:13

score 315 · Answer 10 · 2026-03-23 08:36:48

315

Views

A sufficient and necessary condition for $\mathbb{C}(f(x),g(x))=\mathbb{C}(x)$?

Published on 23 Mar 2026 - 8:36

score 46 · Answer 11 · 2026-03-28 06:24:00

46

Views

Basis for field extension of $\mathbb{F}_{p^n}$ over $\mathbb{F}_p$

Published on 28 Mar 2026 - 6:24

score 103 · Answer 12 · 2026-03-28 04:53:12

103

Views

$L/K$ is a normal field extension , $H=\operatorname{Aut}(L/K)$ proof that $L/L^{H}$ is separable extension

Published on 28 Mar 2026 - 4:53

score 181 · Answer 13 · 2026-03-26 02:46:47

181

Views

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

Published on 26 Mar 2026 - 2:46

score 395 · Answer 14 · 2026-03-28 06:24:09

395

Views

Show that $(9-5\sqrt 3)(2-\sqrt 2) $ is not a square in $\mathbb Q (\sqrt 2, \sqrt 3) $

Published on 28 Mar 2026 - 6:24

score 108 · Answer 15 · 2026-03-28 06:41:50

For an irreducible quartic over $K $of char $0$ with root $u $ there is no proper field between $K $ and $K (u) $ iff Gal$(F/K)$ is $A_4$ or $S_4$

List Question

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

Constructing composite Galois field with arbitrary primitive polynomial?

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

Show that this Galois group is solvable (Base case)

Prove this homomorphism gives an equivalent definition of Linear Space

How to solve a system of equations in a field

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.

Galois group of the general (indeterminate) polynomial equation

A sufficient and necessary condition for $\mathbb{C}(f(x),g(x))=\mathbb{C}(x)$?

Basis for field extension of $\mathbb{F}_{p^n}$ over $\mathbb{F}_p$

$L/K$ is a normal field extension , $H=\operatorname{Aut}(L/K)$ proof that $L/L^{H}$ is separable extension

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

Show that $(9-5\sqrt 3)(2-\sqrt 2) $ is not a square in $\mathbb Q (\sqrt 2, \sqrt 3) $

For an irreducible quartic over $K $of char $0$ with root $u $ there is no proper field between $K $ and $K (u) $ iff Gal$(F/K)$ is $A_4$ or $S_4$

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