Almost Cohen-Macaulayness of Koszul homology

摘要

Let (R,m) be a commutative Noetherian ring, I an ideal of R and M a non-zero finitely generated R-module. We show that if M and H0(I,M) are aCM R-modules and I=(x1,…,xn+1) such that x1,…,xn is an M-regular sequence, then Hi(I,M) is an aCM R-module for all i. Moreover, we prove that if R and Hi(I,R) are aCM for all i, then R/(0:I) is aCM. In addition, we prove that if R is aCM and x1,…,xn is an aCM d-sequence, then depth Hi(x1,…,xn;R)≥i?1 for all i.