Question

What is an exact field?

score 197 · Answer 1 · 2026-04-10 02:26:12

197

Views

What is an exact field?

Published on 10 Apr 2026 - 2:26

score 141 · Answer 2 · 2026-04-17 10:17:41

141

Views

Determining all extensions of a field morphism

Published on 17 Apr 2026 - 10:17

score 46 · Answer 3 · 2026-04-15 13:50:16

46

Views

Free, linearly disjoint field extensions and algebraic/separable closures

Published on 15 Apr 2026 - 13:50

score 71 · Answer 4 · 2026-04-14 08:59:16

71

Views

Prove that $f$ is irreducible if it has no roots in a finite field $F$.

Published on 14 Apr 2026 - 8:59

score 109 · Answer 5 · 2026-04-16 07:13:12

109

Views

How to determine the degree of the extension $\mathbb{Q}(\sqrt[3] 2,i)$ over $\mathbb{Q}$? and what is the form of these?

Published on 16 Apr 2026 - 7:13

score 96 · Answer 6 · 2026-04-16 18:02:37

96

Views

$\mathbb{Q}(\alpha, \sqrt 2)$ = $\mathbb{Q}(\alpha \sqrt 2)$, where $\alpha$ is a root of $ x^3 −x^2 + 1$?

Published on 16 Apr 2026 - 18:02

score 76 · Answer 7 · 2026-04-13 18:23:03

76

Views

Is there a notion of an "Lie (algebraic) skew field" and can it be shown that $\mathbb R^3$ isn't one?

Published on 13 Apr 2026 - 18:23

score 139 · Answer 8 · 2026-04-16 03:32:33

139

Views

Are the roots of $X^4+X^3-2$ constructible?

Published on 16 Apr 2026 - 3:32

score 64 · Answer 9 · 2026-04-11 02:40:05

64

Views

A Problem about the Artin Symbol

Published on 11 Apr 2026 - 2:40

score 62 · Answer 10 · 2026-04-12 22:43:51

62

Views

Generator of Selmer group of a field $K(S,2)=\{b \in K^{\times}/{K^{\times}}^2\mid v(b)≡0 \bmod2, \forall v \notin S\}$

Published on 12 Apr 2026 - 22:43

score 119 · Answer 11 · 2026-04-15 12:28:01

119

Views

Is it true that $\mathbb{Q}(\sqrt{3}+\sqrt{5})= \mathbb{Q}(\sqrt{3+\sqrt{5}})$

Published on 15 Apr 2026 - 12:28

score 208 · Answer 12 · 2026-05-11 09:35:43

208

Views

Can the field of real numbers be ordered in more than one way?

Published on 11 May 2026 - 9:35

score 1.1k · Answer 13 · 2026-04-13 18:22:28

1.1k

Views

Is there a finite abelian group which is not isomorphic to either the additive or multiplicative group of a field?

Published on 13 Apr 2026 - 18:22

score 65 · Answer 14 · 2026-04-09 15:22:18

65

Views

Proof that on infinite fields, finite separable extensions are all simple.

Published on 09 Apr 2026 - 15:22

score 60 · Answer 15 · 2026-03-25 16:14:07

60

Views

Question about automorphisms of the cyclotomic field and Sagemath

Published on 25 Mar 2026 - 16:14

List Question

What is an exact field?

Determining all extensions of a field morphism

Free, linearly disjoint field extensions and algebraic/separable closures

Prove that $f$ is irreducible if it has no roots in a finite field $F$.

How to determine the degree of the extension $\mathbb{Q}(\sqrt[3] 2,i)$ over $\mathbb{Q}$? and what is the form of these?

$\mathbb{Q}(\alpha, \sqrt 2)$ = $\mathbb{Q}(\alpha \sqrt 2)$, where $\alpha$ is a root of $ x^3 −x^2 + 1$?

Is there a notion of an "Lie (algebraic) skew field" and can it be shown that $\mathbb R^3$ isn't one?

Are the roots of $X^4+X^3-2$ constructible?

A Problem about the Artin Symbol

Generator of Selmer group of a field $K(S,2)=\{b \in K^{\times}/{K^{\times}}^2\mid v(b)≡0 \bmod2, \forall v \notin S\}$

Is it true that $\mathbb{Q}(\sqrt{3}+\sqrt{5})= \mathbb{Q}(\sqrt{3+\sqrt{5}})$

Can the field of real numbers be ordered in more than one way?

Is there a finite abelian group which is not isomorphic to either the additive or multiplicative group of a field?

Proof that on infinite fields, finite separable extensions are all simple.

Question about automorphisms of the cyclotomic field and Sagemath

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