Description
Title : Asymptotic prime divisors.
Abstract : Consider a Noetherian ring R and an ideal I of R. Ratliff asked
a question that what happens to Ass(R/I^n) as n gets large ? He was able
to answer that question for the integral closure of I. Meanwhile Brodmann
answered the original question, and proved that the set Ass(R/I^n)
stabilizes for large n.
We will discuss the proof of stability of Ass(R/I^n). We will also
give an example to show that the sequence is not monotone. The aim of
this
series of talk to present the first chapter of S. McAdam, Asymptotic
prime divisors, Lecture Notes in Mathematics 1023, Springer-Verlag,
Berlin, 1983.