Let $k$ be an algebraically closed field, And let $V(\mathfrak{a})$ be the algebraic variety generated by the ideal $\mathfrak{a} \subset k[x_1,\cdots,x_n]$. I have read that we can identify $V(\mathfrak{a})$ as
$V(\mathfrak{a})=\text{Hom}_{k-alg}( k[x_1,\cdots,x_n]/ \mathfrak{a} , k)$.
But I don't see how. I know that the points of $V(\mathfrak{a})$ is in bijection with the maximal ideals of $k[x_1,\cdots,x_n]/ \mathfrak{a}$ by Hilbert's Nullstellenstaz, but I don't see how to view it as $k$-algebra homomorphism.