§ In a PID, all prime ideals are maximal, geometrically

Assume RR is Noetherian. In a drawing, it would look like this:
NO IDEALS ABOVE  : height 2
(p0)  (p1) (p2)  : height 1
      (0)        : height 0
So each pi is maximal. This is a geometric way of noting that in a principal ideal domain, prime ideals are maximal.

§ References