Characterizing local rings via perfect and coperfect modules

Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using the classes $ \mathcal{P}_C $ and $ \mathcal{I}_C $, we extend the notions of perfect and coperfect modules introduced by D.Rees \cite{R} and O.Jenda \cite{J1}. First, we study the basic properties of these modules and relations between them. Next, we characterize local rings in terms of the existence of special perfect (resp. coperfect) modules.