Question

$G$ be a finite subgroup of $Aut(K)$ , $F:=\{x\in K : f(x)=x , \forall f \in G\}$ . Then is $[K:F]$ finite ?

score 61 · Answer 1 · 2026-04-16 20:07:18

61

Views

$G$ be a finite subgroup of $Aut(K)$ , $F:=\{x\in K : f(x)=x , \forall f \in G\}$ . Then is $[K:F]$ finite ?

Published on 16 Apr 2026 - 20:07

score 562 · Answer 2 · 2026-04-15 18:44:24

562

Views

$F$ is purely inseparable over $K$ if and only if the only $K$-monomorphism $F \to C$ is the inclusion map.

Published on 15 Apr 2026 - 18:44

score 293 · Answer 3 · 2026-04-17 07:40:28

293

Views

Definition of the term "Lattice of field extension"

Published on 17 Apr 2026 - 7:40

score 137 · Answer 4 · 2026-04-25 18:12:51

137

Views

A statement about normal basis element , trace and characteristic of field

Published on 25 Apr 2026 - 18:12

score 63 · Answer 5 · 2026-04-17 00:36:37

63

Views

$[F:K]$ finite , $Aut_K(F)=\{f_1,...,f_n\}$ , there is $a\in F$ such that $\{f_1(a),...,f_n(a)\}$ forms a basis for $F$ over $K$ ; is $F/K$ Galois?

Published on 17 Apr 2026 - 0:36

score 103 · Answer 6 · 2026-04-16 13:08:49

103

Views

Find the $[\Bbb{R} ^{\text{alg}}:\Bbb{Q}]$

Published on 16 Apr 2026 - 13:08

score 33 · Answer 7 · 2026-04-13 14:43:09

33

Views

Fields - simple question

Published on 13 Apr 2026 - 14:43

score 383 · Answer 8 · 2026-04-16 15:44:55

383

Views

examples of étale algebras $ \mathbb{Q}[\sqrt[3]{2}] \times \mathbb{Q}[\sqrt[3]{5}]$

Published on 16 Apr 2026 - 15:44

score 151 · Answer 9 · 2026-04-12 03:36:49

151

Views

$\sigma$ trivial on $K$ and $F'$ $ \implies$ $\sigma$ trivial on $KF'$?

Published on 12 Apr 2026 - 3:36

score 651 · Answer 10 · 2026-04-14 04:12:30

651

Views

$x^p-a$ either has a root or is irreducible

Published on 14 Apr 2026 - 4:12

score 73 · Answer 11 · 2026-04-15 07:28:16

73

Views

If $K[X]\cong K[a]$ then $K(X)\cong K(a)$

Published on 15 Apr 2026 - 7:28

score 81 · Answer 12 · 2026-04-11 06:10:59

81

Views

Proprieties of Kernel of Subring of Field

Published on 11 Apr 2026 - 6:10

score 2.7k · Answer 13 · 2026-04-15 18:40:47

2.7k

Views

Simple extension of $\mathbb{Q} (\sqrt[4]{2},i)$

Published on 15 Apr 2026 - 18:40

score 107 · Answer 14 · 2026-05-11 01:40:29

107

Views

Transcendental Extension decomposition

Published on 11 May 2026 - 1:40

score 98 · Answer 15 · 2026-04-16 06:16:06

98

Views

Finding Galois group for $\mathbb{Q}(\sqrt[4]{3}, \zeta_4)/ \mathbb{Q}$

Published on 16 Apr 2026 - 6:16

List Question

$G$ be a finite subgroup of $Aut(K)$ , $F:=\{x\in K : f(x)=x , \forall f \in G\}$ . Then is $[K:F]$ finite ?

$F$ is purely inseparable over $K$ if and only if the only $K$-monomorphism $F \to C$ is the inclusion map.

Definition of the term "Lattice of field extension"

A statement about normal basis element , trace and characteristic of field

$[F:K]$ finite , $Aut_K(F)=\{f_1,...,f_n\}$ , there is $a\in F$ such that $\{f_1(a),...,f_n(a)\}$ forms a basis for $F$ over $K$ ; is $F/K$ Galois?

Find the $[\Bbb{R} ^{\text{alg}}:\Bbb{Q}]$

Fields - simple question

examples of étale algebras $ \mathbb{Q}[\sqrt[3]{2}] \times \mathbb{Q}[\sqrt[3]{5}]$

$\sigma$ trivial on $K$ and $F'$ $ \implies$ $\sigma$ trivial on $KF'$?

$x^p-a$ either has a root or is irreducible

If $K[X]\cong K[a]$ then $K(X)\cong K(a)$

Proprieties of Kernel of Subring of Field

Simple extension of $\mathbb{Q} (\sqrt[4]{2},i)$

Transcendental Extension decomposition

Finding Galois group for $\mathbb{Q}(\sqrt[4]{3}, \zeta_4)/ \mathbb{Q}$

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