Question

A doubt in understanding a proof in Galois Theory

score 69 · Answer 1 · 2026-03-25 12:29:32

69

Views

A doubt in understanding a proof in Galois Theory

Published on 25 Mar 2026 - 12:29

score 741 · Answer 2 · 2018-04-12 14:01:27

741

Views

Existence of extension of an embedding for an algebraic extension of a field

Published on 12 Apr 2018 - 14:01

score 105 · Answer 3 · 2026-03-25 04:57:31

105

Views

Real roots of cubic polynomial

Published on 25 Mar 2026 - 4:57

score 30 · Answer 4 · 2026-03-25 13:57:49

30

Views

Do all elements in a quadratic extension of $\mathbb Q$ have degree less than or equal to $2$ over $\mathbb Q$?

Published on 25 Mar 2026 - 13:57

score 269 · Answer 5 · 2026-03-25 13:59:45

269

Views

Determine the quadratic number fields $\mathbb Q[\sqrt{d}]$ that contain a primitive $n$-th root of unity, for some integer $n$.

Published on 25 Mar 2026 - 13:59

score 158 · Answer 6 · 2026-03-20 17:27:45

158

Views

The ring generated over the center of a division ring by a group.

Published on 20 Mar 2026 - 17:27

score 56 · Answer 7 · 2026-03-25 09:50:11

56

Views

If $w\in\mathbb{Q}(a,b)$, determine $w$ such that $\mathbb{Q}(w)=\mathbb{Q}(a,b)$ with $a,b\in\mathbb{R}$ and are algebraic over $\mathbb{Q}$

Published on 25 Mar 2026 - 9:50

score 145 · Answer 8 · 2026-03-26 01:34:51

145

Views

Prove that $\forall n \geq 1$ there exists a field containing $n$ subfields

Published on 26 Mar 2026 - 1:34

score 676 · Answer 9 · 2026-03-25 13:58:08

676

Views

If F is a field and a,b are in F, c is in an extension field, show that F(ac+b)=F(c)

Published on 25 Mar 2026 - 13:58

score 313 · Answer 10 · 2018-04-13 18:59:04

313

Views

$\mathbb Q(\sqrt{2},i)=\mathbb Q(\sqrt{-2},i)$

Published on 13 Apr 2018 - 18:59

score 79 · Answer 11 · 2026-03-25 13:59:50

79

Views

$K=F(\alpha)$ if $K$ is a quadratic extension

Published on 25 Mar 2026 - 13:59

score 214 · Answer 12 · 2026-03-25 13:56:57

214

Views

Corollary 15.3.8 from Artin (degrees of field extensions)

Published on 25 Mar 2026 - 13:56

score 29 · Answer 13 · 2018-04-14 00:27:37

29

Views

Domain Property conserved after Tensoring with Transcendental Extension

Published on 14 Apr 2018 - 0:27

score 179 · Answer 14 · 2026-03-27 05:58:03

179

Views

Proving $\mathbb{Q}(r)$ is Galois over $\mathbb{Q}$ ?

Published on 27 Mar 2026 - 5:58

score 902 · Answer 15 · 2026-03-25 22:30:12

902

Views

Field with one element in an elementary context

Published on 25 Mar 2026 - 22:30

List Question

A doubt in understanding a proof in Galois Theory

Existence of extension of an embedding for an algebraic extension of a field

Real roots of cubic polynomial

Do all elements in a quadratic extension of $\mathbb Q$ have degree less than or equal to $2$ over $\mathbb Q$?

Determine the quadratic number fields $\mathbb Q[\sqrt{d}]$ that contain a primitive $n$-th root of unity, for some integer $n$.

The ring generated over the center of a division ring by a group.

If $w\in\mathbb{Q}(a,b)$, determine $w$ such that $\mathbb{Q}(w)=\mathbb{Q}(a,b)$ with $a,b\in\mathbb{R}$ and are algebraic over $\mathbb{Q}$

Prove that $\forall n \geq 1$ there exists a field containing $n$ subfields

If F is a field and a,b are in F, c is in an extension field, show that F(ac+b)=F(c)

$\mathbb Q(\sqrt{2},i)=\mathbb Q(\sqrt{-2},i)$

$K=F(\alpha)$ if $K$ is a quadratic extension

Corollary 15.3.8 from Artin (degrees of field extensions)

Domain Property conserved after Tensoring with Transcendental Extension

Proving $\mathbb{Q}(r)$ is Galois over $\mathbb{Q}$ ?

Field with one element in an elementary context

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