Let $I$ and $J$ be two ideals in $\mathbb C[X,Y]$ such that $\mu(I)=\mu(J) \le 3$ and $I^2=J^2$ . Then is it necessarily true that $I=J$ ? If not, then is it at least true if we assume $I,J$ are homogeneous ideals ?

I believe it should not be true but I am having a hard time finding a counterexample.

Please help

  • $\begingroup$ It sounds interesting, and there is another question similar to this. Where does this question come from? $\endgroup$ – Youngsu Feb 6 at 6:07

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