Is there any example of a $P$primary ideal $I$ in a noetherian domain $R$ such that $I^2=PI \not=P^2$?
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1$\begingroup$ The question seems clear enough now. $I$ is a primary ideal, and $P$, the radical of $I$, is the associated prime ideal. Meta: meta.mathoverflow.net/a/1207/2926 $\endgroup$ – Todd Trimble♦ Nov 24 '13 at 13:31

$\begingroup$ Solved here: math.stackexchange.com/questions/850130/… $\endgroup$ – user26857 Jan 19 '18 at 19:42
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What a fun problem for the holiday season! Yes, an example is $R=\mathbb C[a,b,c,d]/(a^4bd, b^3cd, c^2ad, a^3b^2cd^3) \cong \mathbb C[t^9,t^{13},t^{16},t^{23}]$. Let $I=(a,b,c)$ and $P=(a,b,c,d)$.