Let I be an ideal generated by and in the ring
Show that is different
And
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.
i normally don't answer questions with so many parts and no work done by the OP, because that would be a crime! to get you started:
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