Let (R,m) be a commutative Noetherian local ring and M be a finitely generated R-module of dimension d. Then the following statements hold: (a) If width(Him (M)) i − 1 for all i with 2 i < d, then Hdm (M) is co-Cohen- Macaulay of Noetherian dimension d. (b) If M is an unmixed R-module and depthM d − 1, then Hdm (M) is co- Cohen-Macaulay of Noetherian dimension d if and only if Hd−1 m (M) is either zero or co-Cohen-Macaulay of Noetherian dimension d − 2.
