ON THE ASYMPTOTIC STABILITY OF CERTAIN SETS OF PRIME IDEALS

Abstract

Let (R,m) be a Noetherian local ring, I,J two ideals of R, and M a finitely generated R−module. It is shown that the set AssR(Hd−1 I (Nn))∪ {m} is stable for large n, where we use Nn to denote R−module JnM/Jn+1M or R−module M/JnM and d is the eventual value of dimNn. We also give a counter-example for stability of certain sets of associated prime ideals of Ext−modules and of attached prime ideals of local cohomology modules w.r.t. m