Journal of the
Korean Mathematical Society JKMS

The classes of $G_C$ homological modules over commutative ring, where $C$ is a semidualizing module, extend Holm and J{\o}gensen's notions of $C$-Gorenstein homological modules to the non-Noetherian setting and generalize the classical classes of homological modules and the classes of Gorenstein homological modules within this setting. On the other hand, transfer of homological properties along ring homomorphisms is already a classical field of study. Motivated by the ideas mentioned above, in this article we will investigate the transfer properties of $C$ and $G_C$ homological dimension.

Keywords: semidualizing module, ring homomorphism, $C$ homological modules, $G_C$ homological modules, localization

MSC numbers: 13D05, 13D02, 16E10, 16E30