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A generalization of the cofiniteness problem in local cohomology modules

Part of: Commutative algebra: Homological methods

Published online by Cambridge University Press:  09 April 2009

J. Asadollahi ,
K. Khashyarmanesh  and
SH. Salarian
J. Asadollahi
Affiliation:
Institute for Studies in TheoreticalPhysics and Mathematics P.O. Box 19395-5746, Tehran, Iran and Shahre-e-Kord University, Faculty of Science P.O.Box 115, Shahre-e-Kord, Iran e-mail: Asadollahi@mail.ipm.ir
K. Khashyarmanesh
Affiliation:
Institute for Studies in Theoretical Physics and MathematicsP.O. Box 19395-5746, Tehran, IranDamghan Univesity, Department of Mathematics, P.O. Box 36715-364, Damghan, Iran, e-mail: Khashyar@mail.ipm.irSalarian@mail.ipm.ir.
SH. Salarian
Affiliation:
Institute for Studies in Theoretical Physics and MathematicsP.O. Box 19395-5746, Tehran, IranDamghan Univesity, Department of Mathematics, P.O. Box 36715-364, Damghan, Iran, e-mail: Khashyar@mail.ipm.irSalarian@mail.ipm.ir.
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Abstract

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Let R be a commutative Noetherian ring with nonzero identity and let M be a finitely generated R-module. In this paper, we prove that if an ideal I of R is generated by a u.s.d-sequence on M then the local cohomology module (M) is I-cofinite. Furthermore, for any system of ideals Φ of R, we study the cofiniteness problem in the context of general local cohomology modules.

Keywords

Local cohomologycofinited-sequenceBass number

MSC classification

Secondary: 13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) 13D45: Local cohomology
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 3 , December 2003 , pp. 313 - 324
Copyright
Copyright © Australian Mathematical Society 2003

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