“School of Mathematics”
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| Paper IPM / M / 8433 |
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| Abstract: | |
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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 aM ≠ M.
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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