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, 130:425 | Cite as

Characterization of modules of finite projective dimension via Frobenius functors

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Article

Abstract

Let M be a finitely generated module over a local ring R of characteristic p > 0. If depth(R) = s, then the property that M has finite projective dimension can be characterized by the vanishing of the functor \({{\rm Ext}^i_R(M, ^{f^n}R)}\) for s + 1 consecutive values i > 0 and for infinitely many n. In addition, if R is a d-dimensional complete intersection, then M has finite projective dimension can be characterized by the vanishing of the functor \({{\rm Ext}^i_R(M, ^{f^n}R)}\) for some i ≥ d and some n > 0.

Mathematics Subject Classification (2000)

13H10 13D07 13D02 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Saeed Nasseh
    • 1
    • 2
  • Massoud Tousi
    • 1
    • 2
  • Siamak Yassemi
    • 1
    • 3
  1. 1.School of MathematicsInstitute for research in fundamental sciences (IPM)TehranIran
  2. 2.Department of MathematicsShahid Beheshti University, G. C.TehranIran
  3. 3.Department of MathematicsUniversity of TehranTehranIran

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