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k -torsionless modules with finite Gorenstein dimension

Maryam SalimiElham TavasoliSiamak Yassemi — 2012

Czechoslovak Mathematical Journal

Let R be a commutative Noetherian ring. It is shown that the finitely generated R -module M with finite Gorenstein dimension is reflexive if and only if M 𝔭 is reflexive for 𝔭 Spec ( R ) with depth ( R 𝔭 ) 1 , and G- dim R 𝔭 ( M 𝔭 ) depth ( R 𝔭 ) - 2 for 𝔭 Spec ( R ) with depth ( R 𝔭 ) 2 . This gives a generalization of Serre and Samuel’s results on reflexive modules over a regular local ring and a generalization of a recent result due to Belshoff. In addition, for n 2 we give a characterization of n -Gorenstein rings via Gorenstein dimension of the dual of modules. Finally it is shown...

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