Journal of the
Korean Mathematical Society JKMS

Let $S$ and $R$ be rings and $_{S}C_{R}$ a semidualizing bimodule. We introduce the notion of $G_C$-$FP_n$-injective modules, which generalizes $G_C$-$FP$-injective modules and $G_C$-weak injective modules. The homological properties and the stability of $G_C$-$FP_n$-injective modules are investigated. When $S$ is a left $n$-coherent ring, several nice properties and new Foxby equivalences relative to $G_C$-$FP_n$-injective modules are given.

Keywords: Semidualizing bimodule, $G_C$-$FP_n$-injective module, $n$-coherent ring, stability of category, Foxby equivalence

MSC numbers: Primary 18G05, 18G25, 16E30

Supported by: This work was financially supported by NSFC (12061026).