THE STABILITY OF CERTAIN SETS OF ATTACHED PRIME IDEALS RELATED TO COSEQUENCE IN DIMENSION > k

Abstract

Abstract. Let (R, m) be a Noetherian local ring, I, J two ideals of R, and A an Artinian R-module. Let k ≥ 0 be an integer and r = Width >k (I, A) the supremum of lengths of A-cosequences in dimension > k in I defined by . It is first shown that for each t ≤ r and each sequence x 1 , . . . , xt which is an A-cosequence in dimension > k, the setis independent of the choice of n 1 , . . . , nt. Let r be the eventual value of Width >k (0 : A J n ). Then our second result says that for each t ≤ r the set (Att R (Tor R i (R/I, (0 : A J n )))) ≥k is stable for large n.