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Math Help - Unique Factorization Domains

  1. #1
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    Unique Factorization Domains

    Let p be a prime integer.

    Prove that Z_p[x] is a unique factorization domain.

    I need a legit proof to this if possible.
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  2. #2
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    Prove that Z_p is a unique factorization domain for prime p.

    Quote Originally Posted by pleasehelpme1 View Post
    Let p be a prime integer.

    Prove that Z_p[x] is a unique factorization domain.

    I need a legit proof to this if possible.
    \mathbb{Z}_p is a field and so \mathbb{Z}_p[x] is a PID. now try to recall that every PID is a UFD.
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  3. #3
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    ???

    why is this always the answer i get... you can just assume things like Z_p being a field. I don't see how that proves anything?
    Last edited by mr fantastic; December 18th 2009 at 04:49 PM. Reason: Modified tone.
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  4. #4
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    Quote Originally Posted by pleasehelpme1 View Post
    Prove that every irreducible is prime in Z_p where p is prime.

    You are aware of the fact that \mathbb{Z}_p is a FIELD for any prime p ?? Because if you are then your question is trivial, and if you aren't then perhaps try to prove it: it isn't hard.

    Tonio
    Last edited by mr fantastic; December 18th 2009 at 04:42 PM. Reason: No edit - just flagging post as moved from another thread created by duplicate post by OP
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  5. #5
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    Quote Originally Posted by pleasehelpme1 View Post
    Let p prime.

    Prove that Z_p is a unique factorization domain.
    a field is a PID and a PID is a UFD. (take a look at your lecture notes!)
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  6. #6
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    ....

    i can't use that assumption. i have to prove it as if i don't know anything above.
    Last edited by mr fantastic; December 18th 2009 at 04:39 PM. Reason: Modified tone of post.
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  7. #7
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    This whole question is alewady under discussion here: http://www.mathhelpforum.com/math-he...need-help.html

    Thread closed.
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