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Let $R$ be a commutative ring of finite Krull dimension $n$. I'm interested in results where those minimal primes $P$ of $R$ play a role that sit at the end of a prime chain of maximal length, i.e. $$P=P_n \varsubsetneqq ... \varsubsetneqq P_0.$$

Examples are:

  • $\dim(R/P) = \dim R$
  • Additivity and reduction formula for multiplicity $$e(I;M) = \sum_Pe(I;R/P)\lambda(M_P)$$

BTW: Do these primes have a particular name ?

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  • $\begingroup$ "Minimal primes of maximal dimension". $\endgroup$
    – Graham Leuschke
    Commented Nov 8, 2011 at 12:55
  • $\begingroup$ Or just "primes of maximal dimension". $\endgroup$
    – George Lowther
    Commented Nov 9, 2011 at 0:52
  • $\begingroup$ ..although a quick google search suggests that "minimal primes of maximal dimension" may be more common. $\endgroup$
    – George Lowther
    Commented Nov 9, 2011 at 1:02
  • $\begingroup$ Avoid them in a local ring, inductively, using the Prime Avoidance Lemma, and you will have a system of parameters in your hand! $\endgroup$
    – Mahdi Majidi-Zolbanin
    Commented Nov 12, 2011 at 23:38

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