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

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

2010-08-22

arxiv.org/abs/1008.3680v2

Mathematics

Commutative Algebra

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

Scientific paper

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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