List questions from transcendence-degree

Published on 10 Jan 2020 - 12:46

56

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Minimal polynomial of $b$ over $k[a+b,c+d]$

Published on 02 Mar 2020 - 23:26

80

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Concerning $k \subset L \subset k(x,y)$

Published on 02 Mar 2020 - 23:44

21

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Form of $u,v \in \mathbb{C}[x,y]$ satisfying $\mathbb{C}(s_1,s_2,k_1,k_2)=\mathbb{C}(u,v)$

Published on 03 Mar 2020 - 23:24

87

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If $k\subset F\subset E $ is a tower of fields, prove that $\operatorname{tr\,deg}(E/k) =\operatorname{tr\,deg}(E/F) +\operatorname{tr\,deg}(F/k).$

Published on 13 Apr 2020 - 12:27

1.1k

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Two algebraically closed fields are isomorphic if and only if they have the same transcendence degree over their prime fields.

Published on 13 Apr 2020 - 14:59

131

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On a special kind of Discrete Valuation Ring

Published on 15 May 2020 - 3:21

148

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Field of rational functions at a non singular point

Published on 19 May 2020 - 18:31

1.4k

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Understanding the dimension of a variety and transcendence degree

Published on 18 Oct 2016 - 3:18

47

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Reference for automorphisms of field extensions with non-zero transcendence degree

Published on 11 Mar 2017 - 22:40

17

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Let $L = F(S)$ for $S \subseteq L$. Does there exists a transcendental basis $T \subseteq S$ with $F(S) = F(T)$?

Published on 15 Feb 2023 - 20:45

13

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What is $\text{trdeg}(F( X_i Y_j \mid 1 \leq i \leq n, 1 \leq j \leq m) / F)$?

Published on 29 May 2023 - 10:52

135

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How is the field extension finite

Published on 13 Jun 2023 - 18:37

58

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Transcendence degree of $F(x)$ over a field $F$

Published on 15 Mar 2024 - 14:21

205

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Two field extensions of transcendence degree 1

Published on 08 Jun 2017 - 13:51

List Question

Transcendence degree and Krull dimension of finitely generated algebras

Minimal polynomial of $b$ over $k[a+b,c+d]$

Concerning $k \subset L \subset k(x,y)$

Form of $u,v \in \mathbb{C}[x,y]$ satisfying $\mathbb{C}(s_1,s_2,k_1,k_2)=\mathbb{C}(u,v)$

If $k\subset F\subset E $ is a tower of fields, prove that $\operatorname{tr\,deg}(E/k) =\operatorname{tr\,deg}(E/F) +\operatorname{tr\,deg}(F/k).$

Two algebraically closed fields are isomorphic if and only if they have the same transcendence degree over their prime fields.

On a special kind of Discrete Valuation Ring

Field of rational functions at a non singular point

Understanding the dimension of a variety and transcendence degree

Reference for automorphisms of field extensions with non-zero transcendence degree

Let $L = F(S)$ for $S \subseteq L$. Does there exists a transcendental basis $T \subseteq S$ with $F(S) = F(T)$?

What is $\text{trdeg}(F( X_i Y_j \mid 1 \leq i \leq n, 1 \leq j \leq m) / F)$?

How is the field extension finite

Transcendence degree of $F(x)$ over a field $F$

Two field extensions of transcendence degree 1

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