All Questions
3 questions
10
votes
1
answer
243
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If $E_\text{sep}/F$ is normal, then must $E/F$ be normal?
This question has been asked in Math.StackExchange (see here) for more than a week and I even put a bounty on it. But still it hasn't been correctly answered (the current answer there was written by ...
- 452
0
votes
1
answer
473
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A subfield $R \subseteq \mathbb{C}(x,y)$ with 'many' generators $w$, $R(w)=\mathbb{C}(x,y)$
Let $R \subseteq \mathbb{C}(x,y)$ and assume that $R=\mathbb{C}(u,v)$, where $u,v \in \mathbb{C}[x,y]$ are algebraically independent over $\mathbb{C}$.
Here $\mathbb{N}$ includes $0$.
Assume that $R$ ...
- 2,837
3
votes
0
answers
111
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A bound for $[\mathbb{C}(x,y,z):\mathbb{C}(p,q,r)]$, where $\operatorname{Jac}(p,q,r) \in \mathbb{C}^{\times}$
Y. Zhang (in his PhD thesis) and P. I. Katsylo proved the following nice result; the two proofs are different, see: Zhang's thesis and Katsylo's paper:
Let $f: (x,y) \mapsto (p,q)$ be a $k$-algebra ...
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