Question

A solution of a linear system in some extension field implies a solution in the subfield

score 743 · Answer 1 · 2014-05-16 15:37:37

743

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A solution of a linear system in some extension field implies a solution in the subfield

Published on 16 May 2014 - 15:37

score 69 · Answer 2 · 2026-03-25 23:23:31

69

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Let $K = $ algebraic numbers. Then is $\operatorname{Span}_K(\pi, \pi^2, \dots)$ a vector space of transcendentals?

Published on 25 Mar 2026 - 23:23

score 53 · Answer 3 · 2014-05-18 04:47:14

53

Views

Is $\Bbb{R}$ finitely generated over the algebraics?

Published on 18 May 2014 - 4:47

score 1.2k · Answer 4 · 2014-05-18 07:50:13

1.2k

Views

If $f(x)\in F[x]$ is solvable by radicals then its Galois group $Gal(E/F)$ is solvable.

Published on 18 May 2014 - 7:50

score 119 · Answer 5 · 2014-05-19 15:56:23

119

Views

A question about Galois extension

Published on 19 May 2014 - 15:56

score 2.3k · Answer 6 · 2014-05-19 16:41:55

2.3k

Views

Prove that the only automorphism of $\mathbb{Q}(\sqrt[3]{2})$ is the identity automorphism.

Published on 19 May 2014 - 16:41

score 58 · Answer 7 · 2014-05-19 23:29:43

58

Views

E is a Galois extension of F

Published on 19 May 2014 - 23:29

score 147 · Answer 8 · 2014-05-20 10:46:35

147

Views

$L=K(\alpha)$ with $\alpha^p-\alpha=a\in K$

Published on 20 May 2014 - 10:46

score 4.7k · Answer 9 · 2026-03-25 00:53:20

4.7k

Views

Why there is much interest in the study of $\operatorname{Gal}\left(\overline{\mathbb Q}/\mathbb Q\right)$?

Published on 25 Mar 2026 - 0:53

score 1.4k · Answer 10 · 2014-05-25 00:29:49

1.4k

Views

Galois group - extend homomorphism to automorphism

Published on 25 May 2014 - 0:29

score 75 · Answer 11 · 2014-05-25 23:34:20

75

Views

Algebraic extension of an abelian group.

Published on 25 May 2014 - 23:34

score 70 · Answer 12 · 2014-05-26 16:51:24

70

Views

Recognising to be a field

Published on 26 May 2014 - 16:51

score 97 · Answer 13 · 2014-05-27 19:02:21

97

Views

Proving that $\mid Gal(E/F)\mid\leq [E:F]$ by induction

Published on 27 May 2014 - 19:02

score 75 · Answer 14 · 2014-05-27 20:44:08

75

Views

A result on extension fields in linear algebra.

Published on 27 May 2014 - 20:44

score 101 · Answer 15 · 2026-03-30 12:02:39

101

Views

Prove that $\alpha_{1} ^k+ \alpha_{2} ^k +.....+ \alpha_{n} ^k = n$ for $k=0$ and $0$ for $k = 1,2,....,n-1$?

Published on 30 Mar 2026 - 12:02

List Question

A solution of a linear system in some extension field implies a solution in the subfield

Let $K = $ algebraic numbers. Then is $\operatorname{Span}_K(\pi, \pi^2, \dots)$ a vector space of transcendentals?

Is $\Bbb{R}$ finitely generated over the algebraics?

If $f(x)\in F[x]$ is solvable by radicals then its Galois group $Gal(E/F)$ is solvable.

A question about Galois extension

Prove that the only automorphism of $\mathbb{Q}(\sqrt[3]{2})$ is the identity automorphism.

E is a Galois extension of F

$L=K(\alpha)$ with $\alpha^p-\alpha=a\in K$

Why there is much interest in the study of $\operatorname{Gal}\left(\overline{\mathbb Q}/\mathbb Q\right)$?

Galois group - extend homomorphism to automorphism

Algebraic extension of an abelian group.

Recognising to be a field

Proving that $\mid Gal(E/F)\mid\leq [E:F]$ by induction

A result on extension fields in linear algebra.

Prove that $\alpha_{1} ^k+ \alpha_{2} ^k +.....+ \alpha_{n} ^k = n$ for $k=0$ and $0$ for $k = 1,2,....,n-1$?

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