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Thread: Intersection of Ideals

  1. #1
    Junior Member
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    Intersection of Ideals

    True or False:

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

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