ON THE k-REGULAR SEQUENCES AND THE GENERALIZATION OF F-MODULES

For a given ideal I of a Noetherian ring R and an arbitrary integer k ≥ -1, we apply the concept of k-regular sequences and the notion of k-depth to give some results on modules called k-Cohen Macaulay modules, which in local case, is exactly the k-modules (as a generalization of f-modules). Meanwhi...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society pp. 1083 - 1096
Main Authors Khadijeh Ahmadi-Amoli, Navid Sanaei
Format Journal Article
LanguageEnglish
Published 대한수학회 01.09.2012
Subjects
수학
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Summary:For a given ideal I of a Noetherian ring R and an arbitrary integer k ≥ -1, we apply the concept of k-regular sequences and the notion of k-depth to give some results on modules called k-Cohen Macaulay modules, which in local case, is exactly the k-modules (as a generalization of f-modules). Meanwhile, we give an expression of local cohomology with respect to any k-regular sequence in I, in a particular case. We prove that the dimension of homology modules of the Koszul complex with respect to any k-regular sequence is at most k. Therefore homology modules of the Koszul complex with respect to any lter regular sequence has nite length. KCI Citation Count: 0
Bibliography:G704-000208.2012.49.5.005
ISSN:0304-9914
2234-3008
DOI:10.4134/JKMS.2012.49.5.1083