Finding a Noether Normalization for

Question

I have difficulty on how to find Noether normalization of the following

You need to find a maximal algebraically independent set. Do you really have no idea how to do this? You can't find even 1 transcendental element? — Trevor Gunn, Nov 25 '17 at 18:51
For the first one, $x^2 - yz$ is a monic polynomial in which variable? For the second, both $x$ and $y$ are transcendental but if you choose either of them are you left with an integral extension? So what might you need to do? — Trevor Gunn, Nov 25 '17 at 19:18
To help "exercise it on other problems,", here is another similar question, and another one — rschwieb, Nov 27 '17 at 21:15

score 1 · Answer 1 · answered Nov 25 '17 at 19:19

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Hint: the first one is a surface in 3-space, and you can pick a projection on one of the coordinate planes. The other example is similar.

answered Nov 25 '17 at 19:19

1 Answers1