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Homework Help: Homeomorphism of rings

  1. Nov 30, 2005 #1
    Let p,q be two prime numbers. Prove that there exists a homeomorphism of rings such that f([1]_p)=[1]_q from Z_p[X] into Z_q[X] if and only if p=q.

    I believe that the converse of the statement is trivial but the implication seems to be obvious? I really don't know what there really is to prove in this.
  2. jcsd
  3. Nov 30, 2005 #2


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    I think you mean homomorphism? Certainly, the converse is trivial but if the implication is obvious, then what is the proof? Note, that the statement that there exists a homomoprhism of rings such that f(1) = 1 is the statement that there exists a homomorphism of rings such that f(1) = 1.
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