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.

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- May 9th 2009, 11:04 AMpeteryellowAlgebraic number theory.
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. - May 9th 2009, 02:27 PMNonCommAlg
i normally don't answer questions with so many parts and no work done by the OP, because that would be a crime! (Nod) 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