A FINITENESS RESULT FOR ATTACHED PRIMES OF ARTINIAN LOCAL COHOMOLOGY MODULES

摘要

Let (R, m) be a Noetherian local ring. For an integer s≥-1 and an Artinian R-module A, we introduce the notion of A-cosequence in dimension > s and show that the set of all attached primes p ∈U_(n1,...,nk) Att_R(0:A(x_1~(n1),...,x_k~(nk))R) satisfying dim(R/p)≥S is a finite set whenever (x_1,..., x_k) is an A-cosequence in dimension > s. As an application, we give a finiteness result for attached primes of certain Artinian local cohomology modules of a finitely generated R-module.