Mafi, Amir, Some criteria for the Cohen-Macaulay property and local cohomology, Acta mathematica Sinica. English series (Print) , 25(6), 2009, pp. 917-922
Let a be an ideal of a commutative Noetherian ring R and M be a finitely generated R-module of dimension d. We characterize Cohen-Macaulay rings in term of a special homological dimension. Lastly, we prove that if R is a complete local ring, then the Matlis dual of top local cohomology module H d a (M) is a Cohen-Macaulay R-module provided that the R-module M satisfies some conditions.