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Math Help - atomic factorization

  1. #1
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    atomic factorization

    Let m in Z, where m is not a square in Z
    Define N: Z[sqrt(m)]---> N
    Suppose that : a belongs to Z [sqrt(m)]. If N(a) is a prime in N . Show that a is an atom in Z [sqrt(m)]. Give an example of an m and a in Z [sqrt(m)] such that a is an atom but N(a) is not a prime

    Can you give me some hints please?

    Thank you
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  2. #2
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    Quote Originally Posted by knguyen2005 View Post
    Let m in Z, where m is not a square in Z
    Define N: Z[sqrt(m)]---> N
    Suppose that : a belongs to Z [sqrt(m)]. If N(a) is a prime in N . Show that a is an atom in Z [sqrt(m)]. Give an example of an m and a in Z [sqrt(m)] such that a is an atom but N(a) is not a prime

    Can you give me some hints please?

    Thank you
    it's a simple fact that you should not expect to receive any help when you did not define the function N for us, although i guess it's just a "norm" function. also, what on god's green earth

    is "atom"? did you mean "irreducible"?
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  3. #3
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    Sorry about that
    N is the natural number and N is a norm.
    Define N: Z[sqrt(m)]---> N be an Euclidean Domain with:
    (i) If a,b belong to Z[sqrt(m)] and a | b then N(a) =<N(b)
    (ii) If a in Z[sqrt(m)] then there exists q,r in Z[sqrt(m)] s.t b= qa + r where either r =0 or r is non zero and N(r) < N(a)

    Anyway, I think I know how to do it now. Thank you so much for your time on this thread.

    Cheers
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