Question

Extending and compositing injective field endomorphisms

score 60 · Answer 1 · 2023-08-08 01:14:40

60

Views

Extending and compositing injective field endomorphisms

Published on 08 Aug 2023 - 1:14

score 30 · Answer 2 · 2023-08-10 07:19:00

30

Views

Is there any criterion for a number field whose every embedding to $\mathbb{C}$ is closed under complex conjugate?

Published on 10 Aug 2023 - 7:19

score 43 · Answer 3 · 2023-08-10 08:56:17

43

Views

Proving without derivative that extension of a characteristic zero field is separable

Published on 10 Aug 2023 - 8:56

score 55 · Answer 4 · 2026-03-30 03:21:28

55

Views

Galois group of an arbitrary field extension

Published on 30 Mar 2026 - 3:21

score 37 · Answer 5 · 2026-03-25 18:55:41

37

Views

Prolongation valuation of non-complete valued field

Published on 25 Mar 2026 - 18:55

score 27 · Answer 6 · 2026-03-25 07:45:06

27

Views

Trivial Artin map on $F(\zeta)_{\frak P}$

Published on 25 Mar 2026 - 7:45

score 51 · Answer 7 · 2023-08-16 22:49:27

51

Views

Group superscript on field

Published on 16 Aug 2023 - 22:49

score 34 · Answer 8 · 2026-03-27 14:02:14

34

Views

linearly disjoint field extensions in terms of algebraic extension

Published on 27 Mar 2026 - 14:02

score 62 · Answer 9 · 2023-09-01 12:34:46

62

Views

Elements of finite extension of fields that are fixed by embeddings into an algebraically closed field

Published on 01 Sep 2023 - 12:34

score 80 · Answer 10 · 2023-09-02 08:56:47

80

Views

$\alpha, \beta\in\mathbb C$ algebraic over $F \subseteq \mathbb{C}$. Prove: $\exists n\in \mathbb{N}$ such that $F(\alpha, \beta) = F(\alpha+n\beta)$

Published on 02 Sep 2023 - 8:56

score 84 · Answer 11 · 2023-09-03 09:07:56

84

Views

On extensions of fields and embeddings

Published on 03 Sep 2023 - 9:07

score 66 · Answer 12 · 2026-03-25 20:34:37

66

Views

Definition of splitting field: Why do we require centrality?

Published on 25 Mar 2026 - 20:34

score 55 · Answer 13 · 2023-09-06 13:08:31

55

Views

Is the image of the regular representation of a finite field extension an algebraic variey?

Published on 06 Sep 2023 - 13:08

score 78 · Answer 14 · 2023-09-09 03:37:34

78

Views

Suppose I have a field extension $K/F$ and the dimension of $K$ over $F$ is 1. Why can I conclude that $K=F$?

Published on 09 Sep 2023 - 3:37

score 116 · Answer 15 · 2023-09-13 11:16:43

116

Views

If $\alpha$ is algebraic over $\mathbb{Q}$, then is it always true that $\mathbb{Q}[\alpha] = \mathbb{Q}(\alpha)$?

Published on 13 Sep 2023 - 11:16

List Question

Extending and compositing injective field endomorphisms

Is there any criterion for a number field whose every embedding to $\mathbb{C}$ is closed under complex conjugate?

Proving without derivative that extension of a characteristic zero field is separable

Galois group of an arbitrary field extension

Prolongation valuation of non-complete valued field

Trivial Artin map on $F(\zeta)_{\frak P}$

Group superscript on field

linearly disjoint field extensions in terms of algebraic extension

Elements of finite extension of fields that are fixed by embeddings into an algebraically closed field

$\alpha, \beta\in\mathbb C$ algebraic over $F \subseteq \mathbb{C}$. Prove: $\exists n\in \mathbb{N}$ such that $F(\alpha, \beta) = F(\alpha+n\beta)$

On extensions of fields and embeddings

Definition of splitting field: Why do we require centrality?

Is the image of the regular representation of a finite field extension an algebraic variey?

Suppose I have a field extension $K/F$ and the dimension of $K$ over $F$ is 1. Why can I conclude that $K=F$?

If $\alpha$ is algebraic over $\mathbb{Q}$, then is it always true that $\mathbb{Q}[\alpha] = \mathbb{Q}(\alpha)$?

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