Residue fields of $\mathbb Z[X_1,...,X_n]$ are always finite ?

Question

Let $\mathfrak m$ be a maximal ideal of $\mathbb Z[X_1,...,X_n]$;

then is it necessarily true that $\mathbb Z[X_1,...,X_n]/\mathfrak m$ is finite ?

Answer 1

Yes, it follows from Zariski's lemma.