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Homework Help: Rings and Fields- how to prove Z[x]/pZ[x] is an integral domain

  1. Feb 27, 2013 #1
    1. The problem statement, all variables and given/known data

    Prove Z[x]/pZ[x] is an integral domain where p is a prime natural number.

    2. Relevant equations

    I've seen in notes that this quotient ring can be isomorphic to (z/p)[x] and this is an integral domain but I don't know how to prove there is an isomorphism between them and how to prove it is an integral domain...

    3. The attempt at a solution
     
  2. jcsd
  3. Feb 27, 2013 #2
    Do you have any suggestion about what the isomorphism will be?? Just write down some map that looks intuitively right, most of the time this works.
     
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