I'm having issues with a question in Artin, more specifically 11.3.3.e.

The question asks:

> 
> Find generators for the kernel of the following map: $\mathbb{C}[x,y,z] \to \mathbb{C}[t]$ given by $x \mapsto t$, $y \mapsto t^2$, $z \mapsto t^3$
> 
> 
> 

Clearly we have $z-x^3$, $y-x^2$, and $z^2-y^3$ as elements of the kernel.

I'm not sure how to proceed. The book uses the division algorithm in the relevant examples, but it only does that for the two-variable case. I can't see how to apply it here and I also have a hard time understanding why it works.
The other four parts were straightforward maps substituting variables for numbers, this is the first that deals with parametrization.