Some Criteria for the Cohen-Macaulay Property and Local Cohomology

Some Criteria for the Cohen—Macaulay Property and Local Cohomology

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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.

作者 Amir MAFI

机构地区 Department of Mathematics Institute for Studies in Theoretical Physics and Mathematics

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第6期917-922,共6页 数学学报（英文版）

基金 a grant from IPM(No.87130024)

关键词 COHEN-MACAULAY Gorenstein flat module local cohomology module Cohen-Macaulay, Gorenstein flat module, local cohomology module

分类号 O154.2 [理学—基础数学]

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Acta Mathematica Sinica,English Series

2009年第6期

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Some Criteria for the Cohen-Macaulay Property and Local Cohomology

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