Let $R$ be a regular local ring of dimension $n$ and let $P$ be a height $i$ prime ideal of $R$, where $1< i\leq n-1$. Can we find elements $x_1,\dots,x_i$ such that $P$ is the only minimal prime containing $x_1,\dots,x_i$?
Regular local ring and a prime ideal generated by a regular sequence up to radical
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algebraic-geometry
commutative-algebra
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0I also thought about it, i had asked a similar question before for which i got a counterexample, so i thought there should be a counterexample for this too, but i cant find it, so now i am not even sure if this is true or false, perhaps it should be false, but i dont know. Thanks Alex for trying. – 2012-07-07
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0Related to [Height one prime ideal of arithmetical rank greater than 1](http://math.stackexchange.com/questions/161170/height-one-prime-ideal-of-arithmetical-rank-greater-than-1/162376#162376). – 2013-04-28