@PedroTamaroff Hi!!! I want to show that if $V$ is an algebraic set of $K^n$, $V$ is irreducible iff I(V) is a prime ideal of $K[x_1, x_2, \dots, x_n]$
So far, I showed that if $V$ is not irreducible, $I(V)$ is not a prime ideal.. How could I continue?