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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2015
- DOI:
- 10.48550/arXiv.1510.01845
- arXiv:
- arXiv:1510.01845
- Bibcode:
- 2015arXiv151001845R
- Keywords:
-
- Mathematics - Commutative Algebra;
- 13C05;
- 13H10;
- 13D05
- E-Print:
- 16 pages, to appear in Journal of Algebra and its Applications. arXiv admin note: text overlap with arXiv:1508.05813