Maximal and Prime Ideal Consider a field $K$. I have seen that the ideal $(Y-X^2,Z-X^3)$ is a prime ideal in $K[X,Y,Z]$. But now I have to see that it is not a maximal ideal. Therefore, I have to find an ideal between $(Y-X^2,Z-X^3)$ and $K[X,Y,Z]$. Could $(X,Y-X^2,Z-X^3)$ be the maximal ideal I am looking for?

Note that $(X,Y-X^2,Z-X^3)=(X,Y,Z)$ and because $(Y-X^2,Z-X^3)\subset (X,Y-X^2,Z-X^3)$, hence $ (Y-X^2,Z-X^3)$ not maximal ideal. 
