There is a nice classification of prime ideals in the ring $\mathbb{Z}[x]$, see this question.
Is there any generalization of this result, on $\mathbb{Z}[x_1,\cdots,x_n]$?
Due to this post, I guess there is not a 'theorem' for large $n$. However, does anyone know the answer for $n=2$?
What are the prime ideals of $\mathbb{Z}[x,y]$?
