Let $\displaystyle V $ be the $\displaystyle y $-axis contained in $\displaystyle \mathbb{R}^2 $ ($\displaystyle V=\mathbb{V}(x) $).

In lecture, my professor said $\displaystyle V $ is irreducible (which makes sense), but I don't know how to show it. One hint he gave us is that "a prime ideal is radical" i.e. if $\displaystyle I $ is prime then $\displaystyle I = \text{Rad}(I) $.

Any insight is much appreciated.