Co-Cohen-Macaulay Modules and Local Cohomology

Abstract

Let (, m) be a commutative Noetherian local ring and let be a finitely generated-module of dimension. Then the following statements hold: (a) if width (m ()) ≥ −1 for all with 2 ≤ < , then m () is co-Cohen-Macaulay of Noetherian dimension ; (b) if is an unmixed-module and depth ≥ − 1, then m () is co-Cohen-Macaulay of Noetherian dimension if and only if −1 m () is either zero or co-Cohen-Macaulay of Noetherian dimension − 2. As consequence, if m () is co-Cohen-Macaulay of Noetherian dimension for all with 0 ≤ < , then m () is co-Cohen-Macaulay of Noetherian dimension .