1. The problem statement, all variables and given/known data Show that there are exactly two minimal prime ideals in k[X,Y]/<XY>. P is a minimal prime ideal if it is prime and every subset of P that is a prime ideal is actually P. k is a field. 3. The attempt at a solution Prime ideals of k[X,Y] are <0> and <f> for irreducibles f. But then doesn't every ideal contain <0>? So how can there be other prime ideals?