Syzygy and torsionless modules with respect to a semidualizing module (Q458405)

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 \textit{M. Auslander} and \textit{M. Bridger} [Mem. Am. Math. Soc. 94, 146 p. (1969; Zbl 0204.36402)]. 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.