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Some criteria for the Cohen-Macaulay property and local cohomology

Research paper by Amir Mafi

Indexed on: 25 May '09Published on: 25 May '09Published in: Acta Mathematica Sinica, English Series



Abstract

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 Had (M) is a Cohen-Macaulay R-module provided that the R-module M satisfies some conditions.