Syzygy and Torsionless Modules with Respect to a Semidualizing Module

摘要

This paper aims at generalizing the notions of "Auslander dual", "ktorsionless" 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.