I'm confused by the following thing I'm reading on the Wikipedia page Affine variety:
Let $X = \operatorname{spec} A$, $Y = \operatorname{spec} B$ where $A$, $B$ are integral domains that are the quotient of the polynomial ring $k[t_1, \dots, t_n]$, k an algebraically closed field.
A morphism of affine varieties: Each $k$-algebra homomorphism $\phi: B \to A$ defines the continuous function $\phi^{\# }:X \to Y$ by $\mathfrak{m} \mapsto \phi^{-1}(\mathfrak{m}$).
But isn't it the case that unless $\phi$ is surjective, $\phi^{-1}(\mathfrak{m})$ needs not be an ideal in $B$?