On modules with finite Gorenstein dimension

Document Type : Research Paper

Author

Department of Mathematics, MARA.C., Islamic Azad University, Marand, Iran

Abstract

Since the seminal work of Auslander and Bridger, the theory of Gorenstein dimension (G-dimension) has undergone substantial development and attracted considerable attention. This paper investigates the relationship between $k$-torsionless modules and modules of finite Gorenstein dimension over commutative Noetherian rings. We establish new results characterizing the homological properties of these modules, providing comprehensive proofs and constructing non-trivial examples. Our main contributions include a duality theorem linking $k$-torsionlessness to Gorenstein dimension and applications to the study of quasi-Gorenstein rings.

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References

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Journal of Mahani Mathematical Research
Volume 15, Issue 1 - Serial Number 33
January 2026
Pages 509-521

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History

  • Receive Date: 20 August 2025
  • Revise Date: 14 October 2025
  • Accept Date: 25 October 2025

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