Artinian cofinite modules over complete Noetherian local rings

Sadeghi, Behrouz; Bahmanpour, Kamal; A'zami, Jafar

doi:10.1007/s10587-013-0059-4

Czech Math J

2013

DOI: 10.1007/s10587-013-0059-4

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Artinian cofinite modules over complete Noetherian local rings

Behrouz Sadeghi

Kamal Bahmanpour

Jafar A'zami

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2015

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Exactness of Ideal Transforms and Annihilators of Top Local Cohomology Modules

Bahmanpour¹

2015

Journal of the Korean Mathematical Society

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Abstract. Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if x 1 , . . . , xt (1 ≤ t ≤ n) be a subset of a system of parameters for M , then the R-module H t (x 1 ,...,xt) (R) is faithful, i.e., Ann H t (x 1 ,...,xt) (R) = 0. Also, it is shown that, if H i I (R) = 0 for all i > dim R − dim R/I, then the R-module H dim R−dim R/I I (R) is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in [10]. Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module H 1 I (M ), when H i I (M ) = 0 for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra D I (R) is a flat Ralgebra.

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Exactness of Ideal Transforms and Annihilators of Top Local Cohomology Modules

Bahmanpour¹

2015

Journal of the Korean Mathematical Society

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Artinian cofinite modules over complete Noetherian local rings

Cited by 1 publication

References 15 publications

Exactness of Ideal Transforms and Annihilators of Top Local Cohomology Modules

Exactness of Ideal Transforms and Annihilators of Top Local Cohomology Modules

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