Let $R$ be a Cohen-Macaulay ring and let $I$ be an ideal of height $n$. Is it true that height of $P$ is $n$ for all minimal primes over $I$?
If the answer to the above question is negative, then is it true for Gorenstein rings?
2026-03-25 19:03:30.1774465410
Are the minimal primes of the same height
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Take $R=K[X,Y,Z]$ and $I=(X,Y)\cap (Z)$.