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Math Help - Intersection of Ideals

  1. #1
    Junior Member
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    Intersection of Ideals

    True or False:

    If R is a noetherian ring and if A and B are subsets of R, then the intersection <A>\cap<B>, of the ideals they generate is generated by a finite subset of A\cap B

    A hint would preferred to the full solution, I just don't know how to start this, thanks.
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  2. #2
    Senior Member
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    Hi

    Perhaps look in k[x,y] for (nice) subsets A,B such that <A>\cap<B>\neq 0 and A\cap B=\emptyset
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