Open Access
Article

manuscripta mathematica

, 130:425

Characterization of modules of finite projective dimension via Frobenius functors

Authors

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

DOI: 10.1007/s00229-009-0296-x

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

Copyright information

© Springer-Verlag 2009