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Prime Ideals of Z/3Z X Z/9Z

  1. Nov 15, 2011 #1
    Having worked on prime ideals recently and finding them for Z_n I was wondering how you can to find all the prime ideals of a multiplication of Z/3Z X Z/9Z or Z/2Z X Z/4Z for example. I'm mostly having trouble starting this problem and feel that if I could get an idea where to start that I could finish off the proof myself.

  2. jcsd
  3. Nov 15, 2011 #2


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    if R is a commutative ring, and P is a prime ideal, then R/P is an integral domain (some authors require R to have unity for both concepts, however Z3 x Z9 has unity, namely (1,1), so does Z2 x Z4).

    what's another name for a finite integral domain?

    (hint #2: is Z9 a field? what about Z3 x Z3? think in terms of possible ring homomorphisms).
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