Radical of product of ideals vs. Product of radicals of ideals
I am required to find ideals I and J such that .
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!