On the relative Cohen-Macaulay modules

2013/03/09 by Zargar, Majid Rahro
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1303.2208

Abstract

Let R be a commutative Noetherian local ring and let \fa be a proper ideal of R. A non-zero finitely generated R-module M is called relative Cohen-Macaulay with respect to \fa if there is precisely one non vanishing local cohomology modules \H_\faⁱ(M) of M. In this paper, as a main result, it is shown that if M is a Gorenstein R--module, then \H_\faⁱ(M)=0 for all i≠ c where c=\h_M\fa is completely encoded in homological properties of \H_\fa^c(M), in particular in its Bass numbers. Notice that, this result provides a generalization of a result of M. Hellus and P. Schenzel which has been proved before, as a main result, in the case where M=R.

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