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Math Help - prime ideal

  1. #1
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    prime ideal

    Let S be a graded ring.
    f : homogeneous element of degree > 0.
    S_f= localized ring T^{-1}S, where T={ f^k|k \ge 0}.
    S_{(f)} = {elements of degree zero in S_f}.
    Then there is 1-to-1 corresponence between homogeneous prime ideals of S which does not contain f and pime ideals of S_{(f)}.

    In my opinion, homogeneous prime ideal P in S may relate to pime ideal (P S_f)\cap S_{(f)}of S_{(f)}.
    But I can't show that any prime ideal of S_{(f)} is of the form (P S_f)\cap S_{(f)}.
    Last edited by Stiger; February 5th 2010 at 07:28 AM.
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