On the left perpendicular category of the modules of finite projective dimension

2010/08/22 by Tokuji Araya, Araya, Tokuji, Kei-ichiro Iima +3
Mathematics · #13C60 #13D05 #13H10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.AC #math.RA #msc:13C60 #msc:13D05 #msc:13H10

paper · pdf · doi:10.48550/arxiv.1008.3680

6 pages; minor changes; to appear in Comm. Algebra

openalex publication_date 2010/08/22 · arxiv created 2011/04/22 · arxiv updated 2011/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we characterize several properties of commutative notherian local rings in terms of the left perpendicular category of the category of finitely generated modules of finite projective dimension. As an application we prove that a local ring is regular if (and only if) there exists a strong test module for projectivity having finite projective dimension. We also obtain corresponding results with respect to a semidualizing module.

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