On the finiteness properties of Matlis duals of local cohomology modules |
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| Authors: | K Khashyarmansh F Khosh-Ahang |
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| Institution: | (1) Department of Mathematics, Ferdowsi University of Mashhad, Centre of Excellence in Analysis on Algebraic Structures (CEAAS), P.O. Box 1159-91775, Mashhad, Iran |
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| Abstract: | Let R be a complete semi-local ring with respect to the topology defined by its Jacobson radical, a an ideal of R, and M a finitely generated R-module. Let D
R
(−) := Hom
R
(−, E), where E is the injective hull of the direct sum of all simple R-modules. If n is a positive integer such that Ext
R
j
(R/a, D
R
(H
a
t
(M))) is finitely generated for all t > n and all j ⩾ 0, then we show that Hom
R
(R/a, D
R
(H
a
n
(M))) is also finitely generated. Specially, the set of prime ideals in Coass
R
(H
a
n
(M)) which contains a is finite.
Next, assume that (R, m) is a complete local ring. We study the finiteness properties of D
R
(H
a
r
(R)) where r is the least integer i such that H
a
r
(R) is not Artinian. |
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| Keywords: | Local cohomology modules cofinite modules associated primes coassociated primes filter regular sequences Matlis duality functor |
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