A generalization of the finiteness problem in local cohomology modules |
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Authors: | Amir Mafi |
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Affiliation: | (1) Department of Mathematics, University of Kurdistan, P.O. Box 416, Sanandaj, Iran;(2) Institute for Studies in Theoretical Physics and Mathematics, P.O. Box, 19395-5746 Tehran, Iran |
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Abstract: | Let a be an ideal of a commutative Noetherian ring R with non-zero identity and let N be a weakly Laskerian R-module and M be a finitely generated R-module. Let t be a non-negative integer. It is shown that if H a i (N) is a weakly Laskerian R-module for all i < t, then Hom R (R/a, H a t (M, N)) is weakly Laskerian R-module. Also, we prove that Ext R i (R/a, H a t )) is weakly Laskerian R-module for all i = 0, 1. In particular, if Supp R (H a i (N)) is a finite set for all i < t, then Ext R i (R/a, H a t (N)) is weakly Laskerian R-module for all i = 0, 1. |
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Keywords: | Local cohomology modules cofiniteness weakly Laskerian spectral sequences |
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