Some duality and equivalence results

Let \((R,\fm)\) be a relative Cohen-Macaulay local ring with respect to an ideal \(\fa\) of \(R\) and set \(c:=\h\fa\). In this paper, we investigate some properties of the Matlis dual \(\H_{\fa}^c(R)^{\vee}\) of the \(R\)-module \(\H_{\fa}^c(R)\) and we show that such modules treat like canonical m...

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Bibliographic Details
Published in:arXiv.org 2015-08
Main Author: Zargar, Majid Rahro
Format: Article
Language:English
Subjects:
Duality theorem
Equivalence
Modules
Online Access:Get full text
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Summary:Let \((R,\fm)\) be a relative Cohen-Macaulay local ring with respect to an ideal \(\fa\) of \(R\) and set \(c:=\h\fa\). In this paper, we investigate some properties of the Matlis dual \(\H_{\fa}^c(R)^{\vee}\) of the \(R\)-module \(\H_{\fa}^c(R)\) and we show that such modules treat like canonical modules over Cohen-Macaulay local rings. Also, we provide some duality and equivalence results with respect to the module \(\H_{\fa}^c(R)^{\vee}\) and so these results lead to achieve generalizations of some known results, such as the Local Duality Theorem, which have been provided over a Cohen-Macaulay local ring which admits a canonical module.
ISSN:2331-8422