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Syzygy and Torsionless Modules with Respect to a Semidualizing Module |
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| Authors: | Maryam Salimi Elham Tavasoli Pouyan Moradifar Siamak Yassemi |
| Institution: | 1. Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran 2. Department of Mathematics, University of Tehran, Tehran, Iran 3. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran |
| Abstract: | This paper aims at generalizing the notions of “Auslander dual”, “k-torsionless” and “k-th syzygy” modules to the relative setting with respect to a semidualizing module. It is shown that the “relative” Auslander dual shares many nice properties with the Auslander dual originally introduced by Auslander and Bridger. It is also shown the interplay between the “relative” version of “k-torsionless” and “k-th syzygy” modules parallels that of k-torsionless and k-th syzygy modules. |
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