Characterizing local rings via perfect and coperfect modules

Abstract

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.

16 pages, to appear in Journal of Algebra and its Applications. arXiv admin note: text overlap with arXiv:1508.05813