On the C-flatness and injectivity of character modules

Abstract

Let $ R, S $ be arbitrary associative rings and $ _RC_S $ a semidualizing bimodule. We give some equivalent characterizations for $ R $ being left coherent (and right perfect) rings, left Noetherian rings and left Artinian rings in terms of the $ C $-($ {\mathop{{{\text{FP}}}}\nolimits} $-)injectivity, flatness and projectivity of character modules of certain left $ S $-modules.

Keywords

• character modules
• c-flatness
• c-projectivity
• c-(fp-)injectivity
• left coherent (and right perfect) rings
• left noetherian rings
• left artinian rings