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Czechoslovak Mathematical Journal

, Volume 62, Issue 3, pp 663–672 | Cite as

k-torsionless modules with finite Gorenstein dimension

  • Maryam Salimi
  • Elham Tavasoli
  • Siamak Yassemi
Article

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.

Keywords

torsionless module reflexive module Gorenstein dimension 

MSC 2010

13D05 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2012

Authors and Affiliations

  1. 1.Department of Mathematics, Science and Research BranchIslamic Azad UniversityTehranIran
  2. 2.Department of MathematicsUniversity of Tehran, and School of mathematics, Institute for research in fundamental sciences (IPM)TehranIran

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