Cofiniteness and Artinianness of certain local cohomology modules

Let R be a commutative Noetherian ring, I ,  J be two ideals of R , M be an R -module and S be a Serre class of R -modules. A positive answer to the Huneke’s conjecture is given for a Noetherian ring R and minimax R -module M of Krull dimension less than 3, with respect to S . There are some results...

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Veröffentlicht in:Ricerche di matematica 2016-06, Vol.65 (1), p.21-36
Hauptverfasser: Aghapournahr, M., Ahmadi-amoli, Kh, Sadeghi, M. Y.
Format: Artikel
Sprache:eng
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Zusammenfassung:Let R be a commutative Noetherian ring, I ,  J be two ideals of R , M be an R -module and S be a Serre class of R -modules. A positive answer to the Huneke’s conjecture is given for a Noetherian ring R and minimax R -module M of Krull dimension less than 3, with respect to S . There are some results on cofiniteness and Artinianness of local cohomology modules with respect to a pair of ideals. For a ZD-module M of finite Krull dimension and an integer n ∈ N , if H I , J i ( M ) ∈ S for all i > n , then H I , J i ( M ) / a j H I , J i ( M ) ∈ S for any a ∈ W ~ ( I , J ) , all i ≥ n , and all j ≥ 0 . By introducing the concept of Serre cohomological dimension of M with respect to ( I ,  J ), for an integer r ∈ N 0 , H I , J j ( R ) ∈ S for all j > r iff H I , J j ( M ) ∈ S for all j > r and any finite R -module M .
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-015-0240-1