Characterizing local rings via perfect and coperfect modules

M. Rahmani; A. -J. Taherizadeh

Characterizing local rings via perfect and coperfect modules

Commutative Algebra 2016-04-08 v2

Authors: M. Rahmani , A. -J. Taherizadeh

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.

Keywords

commutative algebra local cohomology module categories

Cite

@article{arxiv.1510.01845,
  title  = {Characterizing local rings via perfect and coperfect modules},
  author = {M. Rahmani and A. -J. Taherizadeh},
  journal= {arXiv preprint arXiv:1510.01845},
  year   = {2016}
}

Comments

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

Characterizing local rings via perfect and coperfect modules

Abstract

Keywords

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