Question

If $\mathbb{C}(u,v,x^n)=\mathbb{C}(x,y)$, for every $n \geq 1$, then already $\mathbb{C}(u,v)=\mathbb{C}(x,y)$?

score 141 · Answer 1 · 2026-04-14 19:18:36

141

Views

If $\mathbb{C}(u,v,x^n)=\mathbb{C}(x,y)$, for every $n \geq 1$, then already $\mathbb{C}(u,v)=\mathbb{C}(x,y)$?

Published on 14 Apr 2026 - 19:18

score 77 · Answer 2 · 2026-04-14 11:46:34

77

Views

A polynomial problem on $\mathbb Q[X]$

Published on 14 Apr 2026 - 11:46

score 58 · Answer 3 · 2026-04-11 02:59:59

58

Views

Splitting field of multivariable polynomial.

Published on 11 Apr 2026 - 2:59

score 86 · Answer 4 · 2026-05-15 13:04:58

86

Views

Prove a Weaker Version of the Normal Basis Theorem

Published on 15 May 2026 - 13:04

score 59 · Answer 5 · 2026-05-15 13:14:43

59

Views

Determine the degree of a root of $X^p-X-\alpha$ (Serge Lang Algebra exercise VI.29)

Published on 15 May 2026 - 13:14

score 62 · Answer 6 · 2026-04-17 00:57:41

62

Views

How do I prove that the primitive element of a field extension are this way.

Published on 17 Apr 2026 - 0:57

score 44 · Answer 7 · 2026-04-14 11:19:02

44

Views

Concerning $\mathbb{C}(s_1,s_2,w)=\mathbb{C}(x,y)$, where $s_1,s_2$ are symmetric, $w$ is not symmetric

Published on 14 Apr 2026 - 11:19

score 64 · Answer 8 · 2026-04-14 11:47:05

64

Views

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

Published on 14 Apr 2026 - 11:47

score 59 · Answer 9 · 2026-04-14 00:16:13

59

Views

Evariste Galois' proof of the "Primitive Element Theorem"

Published on 14 Apr 2026 - 0:16

score 26 · Answer 10 · 2026-04-13 06:07:32

26

Views

a is separable on F, b is separable on F(a), proof that b is separable on F

Published on 13 Apr 2026 - 6:07

score 83 · Answer 11 · 2026-04-17 04:17:07

83

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 17 Apr 2026 - 4:17

score 40 · Answer 12 · 2026-04-16 03:23:33

40

Views

$F,G,H,K \in \mathbb{C}[x,y]$, $\mathbb{C}(F,G)=\mathbb{C}(H,K)$ imply $\langle F-a,G-b \rangle=\langle H-c,K-d \rangle$, $a,b,c,d \in \mathbb{C}$?

Published on 16 Apr 2026 - 3:23

score 129 · Answer 13 · 2026-04-25 22:25:11

129

Views

Fields of particular cardinality

Published on 25 Apr 2026 - 22:25

score 87 · Answer 14 · 2026-04-13 18:54:05

87

Views

On extensions of fields and embeddings

Published on 13 Apr 2026 - 18:54

score 68 · Answer 15 · 2026-04-14 17:40:56

68

Views

Understand the tensor product over a field

Published on 14 Apr 2026 - 17:40

List Question

If $\mathbb{C}(u,v,x^n)=\mathbb{C}(x,y)$, for every $n \geq 1$, then already $\mathbb{C}(u,v)=\mathbb{C}(x,y)$?

A polynomial problem on $\mathbb Q[X]$

Splitting field of multivariable polynomial.

Prove a Weaker Version of the Normal Basis Theorem

Determine the degree of a root of $X^p-X-\alpha$ (Serge Lang Algebra exercise VI.29)

How do I prove that the primitive element of a field extension are this way.

Concerning $\mathbb{C}(s_1,s_2,w)=\mathbb{C}(x,y)$, where $s_1,s_2$ are symmetric, $w$ is not symmetric

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

Evariste Galois' proof of the "Primitive Element Theorem"

a is separable on F, b is separable on F(a), proof that b is separable on F

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

$F,G,H,K \in \mathbb{C}[x,y]$, $\mathbb{C}(F,G)=\mathbb{C}(H,K)$ imply $\langle F-a,G-b \rangle=\langle H-c,K-d \rangle$, $a,b,c,d \in \mathbb{C}$?

Fields of particular cardinality

On extensions of fields and embeddings

Understand the tensor product over a field

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