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|Paper IPM / M / 15550||
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 of R-module \"\fac(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 \"\fac(R)∨ 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 R-module.
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