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|Paper IPM / M / 14265||
Let \fa be an ideal of a Noetherian local ring R and let C be a semidualizing R-module. For an R-module X, we denote any of the quantities \fdR X, \GfdR X and \GCfdRX by \T(X). Let M be an R-module such that \"\fai(M)=0 for all i ≠ n. It is proved that if \T(X) < ∞, then \T(\"\fan(M)) ≤ \T(M)+n and the equality holds whenever M is finitely generated. With the aid of these results, among other things, we characterize Cohen-Macaulay modules, dualizing modules and Gorenstein rings.
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