Characterizing local rings via perfect and coperfect modules

2015/10/07 by M. Rahmani, Rahmani, M., A. J. Taherizadeh +2
Mathematics · #13C05 #13D05 #13H10 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #msc:13C05 #msc:13D05 #msc:13H10

paper · pdf · doi:10.48550/arxiv.1510.01845

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

openalex publication_date 2015/10/07 · arxiv created 2016/04/07 · arxiv updated 2016/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a Noetherian ring and let C be a semidualizing R-module. In this paper, by using the classes P_C and I_C , we extend the notions of perfect and coperfect modules introduced by D.Rees \citeR and O.Jenda \citeJ1. 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.

Citations

• Dual of Bass numbers and dualizing modules

Related

• Codualizing modules
• Über rein-wesentliche Erweiterungen
• Presentations of rings with non-trivial semidualizing modules
• Characteristic modules over a local ring
• Chains of semidualizing modules