Is there any example of a $P$-primary ideal $I$ in a noetherian domain $R$ such that $I^2=PI \not=P^2$?


1 Answer 1


What a fun problem for the holiday season! Yes, an example is $R=\mathbb C[a,b,c,d]/(a^4-bd, b^3-cd, c^2-ad, a^3b^2c-d^3) \cong \mathbb C[t^9,t^{13},t^{16},t^{23}]$. Let $I=(a,b,c)$ and $P=(a,b,c,d)$.

  • $\begingroup$ For another example see this answer. $\endgroup$
    – user26857
    Jan 19, 2018 at 19:43

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.