A characterization of Cohen-Macaulay modules and local cohomology |
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| Authors: | R Naghipour M Sedghi |
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| Institution: | (1) Department of Mathematics, University of Tabriz, Tabriz, Iran;(2) Department of Mathematics, Azarbaidjan University of Tarbiat Moallem, Azarshahr, Tabriz, Iran |
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| 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 heightN 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.
Received: 3 July 2005 |
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| Keywords: | Primary 13A30 13E05 Secondary 13A02 |
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