摘要
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 Ha^d(M) is a Cohen-Macaulay R-module provided that the R-module M satisfies some conditions.
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 Ha^d(M) is a Cohen-Macaulay R-module provided that the R-module M satisfies some conditions.
基金
a grant from IPM(No.87130024)