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On the Left Perpendicular Category of the Modules of Finite Projective Dimension |
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| Authors: | Tokuji Araya Kei-Ichiro Iima Ryo Takahashi |
| Institution: | 1. Liberal Arts Division , Tokuyama College of Technology, Gakuendai , Shunan , Yamaguchi , Japan araya@tokuyama.ac.jp;3. Department of Liberal Studies , Nara National College of Technology , Yamatokoriyama , Nara , Japan;4. Department of Mathematical Sciences, Faculty of Science , Shinshu University , Matsumoto , Nagano , Japan |
| Abstract: | In this article, we characterize several properties of commutative noetherian 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. |
| Keywords: | Perpendicular category Projective dimension Semidualizing module Strong test module for projectivity Totally reflexive module |