On modules with finite Gorenstein dimension

Sadeqi, Behruz

doi:10.22103/jmmr.2025.25790.1854

On modules with finite Gorenstein dimension

Document Type : Research Paper

Author

Behruz Sadeqi

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

10.22103/jmmr.2025.25790.1854

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.

Keywords

Torsionless modules

Gorenstein dimension

Noetherian rings

Subjects

Algebra

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