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Archiv der Mathematik

, Volume 87, Issue 4, pp 303–308 | Cite as

A characterization of Cohen-Macaulay modules and local cohomology

  • R. Naghipour
  • M. Sedghi
Article

Abstract.

Let R be a commutative Noetherian ring, and let N be a non-zero finitely generated locally quasi-unmixed R-module. In this paper, the main result asserts that N is Cohen-Macaulay if and only if, for any N-proper ideal I of R generated by height N I elements, the set of asymptotic primes of I with respect to N is equal to the set of presistent primes of I with respect to N. In addition, some applications about local cohomology are included.

Mathematics Subject Classification (2000).

Primary 13A30 13E05 Secondary 13A02 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TabrizTabrizIran
  2. 2.Department of MathematicsAzarbaidjan University of Tarbiat MoallemTabrizIran

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