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- W2611248420 abstract "Let R be a commutative Noetherian ring, I⊆J be ideals of R and M be a finitely generated R-module. In this paper it is shown that q(J,M)≤q(I,M)+cd(J,M/IM). Furthermore, it is shown that, for any ideal I of R and any finitely generated R-module M with q(I,M)≤1, the local cohomology modules HIi(M) are I-cofinite for all integers i≥0. As a consequence of this result it is shown that, if q(I,R)≤1, then for any finitely generated R-module M, the local cohomology modules HIi(M) are I-cofinite for all integers i≥0. Finally, it is shown that the category of all I-cofinite R-modules C(R,I)cof is an Abelian subcategory of the category of all R-modules, whenever (R,m) is a complete Noetherian local ring and I is an ideal of R with q(I,R)≤1. These assertions answer affirmatively two questions raised by R. Hartshorne in [16], in the some special cases." @default.
- W2611248420 created "2017-05-12" @default.
- W2611248420 creator A5032279395 @default.
- W2611248420 date "2017-08-01" @default.
- W2611248420 modified "2023-10-12" @default.
- W2611248420 title "Cohomological dimension, cofiniteness and Abelian categories of cofinite modules" @default.
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- W2611248420 doi "https://doi.org/10.1016/j.jalgebra.2017.04.019" @default.
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