List questions from transcendence-degree

Published on 22 Jul 2017 - 9:41

170

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Transcendence degree of the fraction field of $k[G]$ for torsion-free abelian group $G$

Published on 22 Sep 2017 - 7:07

112

Views

Algebraicity of $R_1 \subseteq R_2$, where $R_1$ and $R_2$ have same finite Krull dimension

Published on 04 Dec 2017 - 15:39

668

Views

Let $\bar{\mathbb{Q}}$ be the algebraic closure of $\mathbb{Q}$. What is the cardinality of a transcendental extension $K\setminus \bar{\mathbb{Q}}$?

Published on 08 Dec 2017 - 4:31

144

Views

About transcendence degree of an affine $K$-domain

Published on 30 Aug 2020 - 20:16

64

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How does transcendence degree relate to the closure of an open set?

Published on 28 Oct 2020 - 15:54

82

Views

Proving that a variety has a lower dimension than its ambient space

Published on 20 Nov 2020 - 16:22

90

Views

$\operatorname{Trdeg}(\operatorname{Frac}(R/(a))) =\operatorname{Trdeg}(\operatorname{Frac}(R))-1$

Published on 17 Feb 2021 - 21:56

250

Views

Transcendence basis as subset of generators

Published on 19 Feb 2021 - 21:00

191

Views

Krull Dimension of Affine Curve / Transcendence Degree of Coordinate Ring

Published on 09 Mar 2021 - 16:55

494

Views

Proper subfields of $\mathbb{C}$ isomorphic to $\mathbb{C}$

Published on 21 Apr 2021 - 7:23

149

Views

If $tr. deg. F/K=r$ then $tr.deg. F(x_1,\ldots,x_n)/K(x_1,\ldots,x_n)=r$.

Published on 29 Jul 2021 - 4:19

54

Views

Question about the proof that a function field over a $T_i$ field is a $T_{i+1}$ field

Published on 20 Aug 2021 - 14:06

507

Views

Algebraic independence of elementary symmetric polynomials

Published on 23 Aug 2021 - 15:57

19

Views

Infinite transcendental basic

Published on 10 Oct 2021 - 12:03

List Question

Showing $[K(x):K(\frac{x^5}{1+x})]=5$?

Transcendence degree of the fraction field of $k[G]$ for torsion-free abelian group $G$

Algebraicity of $R_1 \subseteq R_2$, where $R_1$ and $R_2$ have same finite Krull dimension

Let $\bar{\mathbb{Q}}$ be the algebraic closure of $\mathbb{Q}$. What is the cardinality of a transcendental extension $K\setminus \bar{\mathbb{Q}}$?

About transcendence degree of an affine $K$-domain

How does transcendence degree relate to the closure of an open set?

Proving that a variety has a lower dimension than its ambient space

$\operatorname{Trdeg}(\operatorname{Frac}(R/(a))) =\operatorname{Trdeg}(\operatorname{Frac}(R))-1$

Transcendence basis as subset of generators

Krull Dimension of Affine Curve / Transcendence Degree of Coordinate Ring

Proper subfields of $\mathbb{C}$ isomorphic to $\mathbb{C}$

If $tr. deg. F/K=r$ then $tr.deg. F(x_1,\ldots,x_n)/K(x_1,\ldots,x_n)=r$.

Question about the proof that a function field over a $T_i$ field is a $T_{i+1}$ field

Algebraic independence of elementary symmetric polynomials

Infinite transcendental basic

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