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arXiv · 1510.01845

Characterizing local rings via perfect and coperfect modules

M. Rahmani·A. -J. Taherizadeh
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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.

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M. Rahmani, A. -J. Taherizadeh. 2015-10-07. Characterizing local rings via perfect and coperfect modules. https://arxiv.org/abs/1510.01845

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