k-torsionless modules with finite Gorenstein dimension |
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Authors: | Maryam Salimi Elham Tavasoli Siamak Yassemi |
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Institution: | 1. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran 2. Department of Mathematics, University of Tehran, and School of mathematics, Institute for research in fundamental sciences (IPM), Tehran, Iran
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Abstract: | 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 that every R-module has a k-torsionless cover provided R is a k-Gorenstein ring. |
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