Characterizations of some rings with $\mathcal {C}$-projective, $\mathcal {C}$-(FP)-injective and $\mathcal {C}$-flat modules

摘要

summary:Let $R$ be a commutative ring and $\mathcal {C}$ a semidualizing $R$-module. We investigate the relations between $\mathcal {C}$-flat modules and $\mathcal {C}$-FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.