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http://dx.doi.org/10.4134/JKMS.2012.49.5.1083

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

Ahmadi-Amoli, Khadijeh (Department of Mathematics Payame Noor University)
Sanaei, Navid (Department of Mathematics Payame Noor University)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.5, 2012 , pp. 1083-1096 More about this Journal
Abstract
For a given ideal I of a Noetherian ring R and an arbitrary integer ${\kappa}{\geq}-1$, we apply the concept of ${\kappa}$-regular sequences and the notion of ${\kappa}$-depth to give some results on modules called ${\kappa}$-Cohen Macaulay modules, which in local case, is exactly the ${\kappa}$-modules (as a generalization of f-modules). Meanwhile, we give an expression of local cohomology with respect to any ${\kappa}$-regular sequence in I, in a particular case. We prove that the dimension of homology modules of the Koszul complex with respect to any ${\kappa}$-regular sequence is at most ${\kappa}$. Therefore homology modules of the Koszul complex with respect to any filter regular sequence has finite length.
Keywords
${\kappa}$-regular M-sequences; ${\kappa}$-depth; ${\kappa}$-ht; local cohomology modules; ${\kappa}$-Cohen Macaulay modules; f-modules; ${\kappa}$-modules; Koszul complexes;
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