On the Matlis duals of local cohomology modules and modules of generalized fractions |
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Authors: | Kazem Khashyarmanesh |
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Institution: | (1) Faculty of Mathematical Sciences, Teacher Training University, Tehran, Iran;(2) Institute for Theoretical Physics and Mathematics (IPM), Tehran, Iran;(3) Center of Excellence in Biomathematics, School of Mathematics, University of Tehran, P.O. Box 13145-448, Tehran, Iran |
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Abstract: | Let (R, m) be a commutative Noetherian local ring with non-zero identity, a a proper ideal of R and M a finitely generated R-module with aM ≠ M. Let D(−) ≔ Hom
R
(−, E) be the Matlis dual functor, where E ≔ E(R/m) is the injective hull of the residue field R/m. In this paper, by using a complex which involves modules of generalized fractions, we show that, if x
1, …, x
n
is a regular sequence on M contained in α, then H
(x1, …,xnR
n
D(H
a
n
(M))) is a homomorphic image of D(M), where H
b
i
(−) is the i-th local cohomology functor with respect to an ideal b of R. By applying this result, we study some conditions on a certain module of generalized fractions under which D(H
(x1, …,xn)R
n
(D(H
a
n
(M)))) ⋟ D(D(M)). |
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Keywords: | |
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