Article

manuscripta mathematica

, 130:425

First online:

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Characterization of modules of finite projective dimension via Frobenius functors

  • Saeed NassehAffiliated withSchool of Mathematics, Institute for research in fundamental sciences (IPM)Department of Mathematics, Shahid Beheshti University, G. C.
  • , Massoud TousiAffiliated withSchool of Mathematics, Institute for research in fundamental sciences (IPM)Department of Mathematics, Shahid Beheshti University, G. C.
  • , Siamak YassemiAffiliated withSchool of Mathematics, Institute for research in fundamental sciences (IPM)Department of Mathematics, University of Tehran Email author 

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