List questions from transcendence-degree | MathQA

Is the subextension of a purely transcendental extension purely transcendental over the base field?

Published on 29 Oct 2021 - 2:40

Extended of algebraically independent set

Published on 18 Mar 2022 - 15:32

Add and multiplying disjoint algebraically independent sets are still disjoint algebraically independent sets

Published on 20 Mar 2022 - 22:40

transcendental dimension of a variety

Published on 21 May 2022 - 18:52

Find a field extension $K=k(x,y)$ of transcendence degree 1 where $x\notin k(y)$, $y\notin k(x)$ and $K|k$ is purely transcendental

Published on 14 Jun 2022 - 15:19

$L/K$ is algebraic iff its transcendence degree is zero

Published on 09 Aug 2022 - 5:55

Schanuel's Conjecture $\implies $ no surprises on the integers. $2^t+3^t=1 \implies t\notin\overline{\mathbb{Q}}$

Published on 15 Sep 2022 - 3:57

$(r+1)^{\frac{1}{3}}$ transcendental and $s^2-s$ algebraic on $\mathbb{Q}$ then $r$ is transcendental and $s$ algebraic on $\mathbb{Q}$

Published on 16 Sep 2022 - 15:02

If $K=\mathbb{C}(x)(\sqrt{-1-x^2})$, then $K=\mathbb{C}(t)$ where $t=(i-x)^{-1}\sqrt{(-1-x^2)}/(i-x)$?

Published on 27 Sep 2022 - 21:52

Is $\mathbb{R}(x,\sqrt{1+x^2})$ a purely transcendental extension of $\mathbb{R}$?

Published on 30 Sep 2022 - 1:00

Proving $[\mathbb{Q}(m(\alpha)):\mathbb{Q}]\leq[\mathbb{Q}(\alpha):\mathbb{Q}]$

Published on 05 Dec 2022 - 9:56

Degree of a field extension over $\mathbb{C}$

Published on 18 Dec 2022 - 19:10