How do you show that x is a nonzero divisor in C[x,y,z,w]/<yz-xw>?(adsbygoogle = window.adsbygoogle || []).push({});

Here's how one can start off on this problem but I would like a nice way to finish it:

If x were a zero divisor, then there is a function f not in <yz-xw> so that

f*x = g*(yz-xw).

Here's another question which is slightly more interesting:

prove that x is a nonzero divisor in C[x,y,z,w]/<yw-z^2, yz-xw>.

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# Nonzero divisor in a quotient ring

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