Let I be an ideal generated by and in the ring
Show that is different
Show that ideals in do not factor uniquely into prime ideals.
Show that I is a unique prime ideal contaning
Conclude is not a product of prime ideals.
most parts of the problem are easily proved. what you need to know here is that is actually a maximal ideal of your ring. also is
obvious because to prove that you only need to show that for all for that you will need this fact that