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SUMMARY:Irena Swanson (Purdue University)
DTSTART:20210506T203000Z
DTEND:20210506T220000Z
DTSTAMP:20260423T052642Z
UID:FOTR/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FOTR/49/">Nu
 mbers of associated primes of powers of ideals</a>\nby Irena Swanson (Purd
 ue University) as part of Fellowship of the Ring\n\n\nAbstract\nThis talk 
 is about associated primes of powers of ideals in Noetherian commutative r
 ings.  By a result of Brodmann\, for any ideal $I$ in a ring $R$\, the set
  of associated primes of $I^n$ stabilizes for large $n$.  In general\, the
 \nnumber of associated primes can go up or down as $n$ increases.  This ta
 lk is about sequences $\\{a_n\\}$ for which there exists an ideal $I$ in a
  Noetherian commutative ring $R$ such that the number of associated primes
  of $R/I^n$\nis $a_n$.  A family of examples shows that $I$ may be prime a
 nd the number of associated primes of $I^2$ need not be polynomial in the 
 dimension of the ring.\n\nThis is a report on four separate projects with 
 Sarah Weinstein\, Jesse Kim\, Robert Walker\, and ongoing work with Roswit
 ha Rissner.\n
LOCATION:https://researchseminars.org/talk/FOTR/49/
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