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Math Help - Radical of product of ideals vs. Product of radicals of ideals

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    Newbie Naranja's Avatar
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    Red face Radical of product of ideals vs. Product of radicals of ideals

    Hello,

    I am required to find ideals I and J such that \sqrt{IJ} \neq \sqrt{I}\sqrt{J}.

    I have tried working directly from the definitions and trying to find a way to get something in one but not the other, but I can't do it. I'm guessing there's either a very simple counterexample, or it's something complicated. Whatever I try they end up equal.

    Can anyone give me any pointers for what to try? Apologies if I haven't explained well enough, I will try to clarify anything if necessary.

    Thanks very much!
    Last edited by Naranja; March 21st 2014 at 09:24 AM.
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