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Paper   IPM / M / 8433
School of Mathematics
  Title:   On the matlis duals of local cohomology modules
  Author(s):  K. Khashyarmanesh
  Status:   Published
  Journal: Archiv der Mathematik
  Vol.:  88
  Year:  2007
  Pages:   413-418
  Supported by:  IPM
Let (R, \frak m) be a commutative Noetherian local ring with non-zero identity, \frak a an ideal of R and M a finitely generated R-module with \frak aMM. Let D(−):= HomR(−, E) be the Matlis dual functor, where E : = E(R/\frak m) is the injective hull of the residue field R/\frakm. We show that, for a positive integer n, if there exists a regular sequence xl, ... , xn ∈ \frak a and the i-th local cohomology module Hi\fraka(M) of M with respect to \frak a is zero for all i with i > n then Hn\fraka(D(Hn\fraka(M))) = E.

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