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I have been having trouble with an exercise in my abstract algebra course. It is as follows:

Let $f: \mathbb{C}[x,y] \rightarrow \mathbb{C}[t]$ be a homomorphism that is the identity on $\mathbb{C}$ and sends $x$ to $x(t)$ and $y$ to $y(t)$ such that $x(t)$ and $y(t)$ are not both constant. Prove that the kernel of $f$ is a principal ideal.

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    Why did you edit out the definition of $f$? The question doesn't make sense like that. Also, I don't think it has much to do with complex analysis, not directly, anyway.2012-11-26

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