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Math Help - factorial domains

  1. #1
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    factorial domains

    Any thoughts?

    Suppose R is a factorial domain and a and b are in R with a not zero and a and b relatively prime. Show that if a divides bc, c in R, then a divides c.

    Thanks!
    Last edited by mr fantastic; April 30th 2009 at 01:53 PM. Reason: Restored question and closed thread.
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  2. #2
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    Hi

    Lemma (Maybe from Gauss): Let p be an irreducible element in a UFD R, then for any elements a,b in R, p|ab\Rightarrow p|a\ \text{or}\ p|b

    In your case, any element can be written as a (unique) product of irreducible elements.

    a and b relatively prime
    Write what this means, and the solution should come.

    EDIT: As ThePerfectHacker said, what I originally wrote was wrong.
    Last edited by clic-clac; April 30th 2009 at 11:14 PM.
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  3. #3
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    Quote Originally Posted by clic-clac View Post
    Lemma (Maybe from Gauss): Let p be an irreducible element in a ring R, then for any elements a,b in R, p|ab\Rightarrow p|a\ \text{or}\ p|b
    This is not true. If R is a UFD then it is, but not in general.
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