J. Aust. Math. Soc.  75 (2003), 313-324
A generalization of the cofiniteness problem in local cohomology modules

J. Asadollahi
  Institute for Studies in Theoretical
  Physics and Mathematics
  P.O. Box 19395-5746, Tehran
  Iran
  and
  Shahre-e-Kord University
  Faculty of Science
  P.O.Box 115, Shahre-e-Kord
  Iran
  Asadollahi@mail.ipm.ir
K. Khashyarmanesh
  Institute for Studies in Theoretical
  Physics and Mathematics
  P.O. Box 19395-5746, Tehran
  Iran
  and
  Damghan University
  Department of Mathematics
  P.O. Box 36715-364, Damghan
  Iran
  Khashyar@mail.ipm.ir
and
Sh. Salarian
  Institute for Studies in Theoretical
  Physics and Mathematics
  P.O. Box 19395-5746, Tehran
  Iran
  and
  Damghan University
  Department of Mathematics
  P.O. Box 36715-364, Damghan
  Iran
  Salarian@mail.ipm.ir


Abstract
Let $R$ be a commutative Noetherian ring with nonzero identity and let $M$ be a finitely generated $R$-module. In this paper, we prove that if an ideal $I$ of $R$ is generated by a u.s.d-sequence on $M$ then the local cohomology module $H^i_I(M)$ is $I$-cofinite. Furthermore, for any system of ideals $\Phi $ of $R$, we study the cofiniteness problem in the context of general local cohomology modules.
Download the article in PDF format (size 108 Kb)
TeXAdel Scientific Publishing ©  Australian MS