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- W2078303591 abstract "Let R be a commutative Noetherian ring, I an ideal of R and let M and N be non-zero R -modules. It is shown that the R -modules Ext R i ( N , M ) are I -cofinite, for all i ⩾ 0 , whenever M is I -cofinite and N is finitely generated of dimension d ⩽ 2 . Also, we prove that the R -modules Ext R i ( N , M ) are I -cofinite, for all i ⩾ 0 , whenever N is finitely generated and M is I -cofinite of dimension d ⩽ 1 . This immediately implies that if I has dimension one (i.e., dim R / I = 1 ) then Ext R i ( N , H I i ( M ) ) is I -cofinite for all i ⩾ 0 , and all finitely generated R -modules M and N . Also, we prove that if R is local then the R -modules Ext R i ( N , M ) are I -weakly cofinite, for all i ⩾ 0 , whenever M is I -cofinite and N is finitely generated of dimension d ⩽ 3 . Finally, it is shown that the R -modules Ext R i ( N , M ) are I -weakly cofinite, for all i ⩾ 0 , whenever R is local, N is finitely generated and M is I -cofinite of dimension d ⩽ 2 ." @default.
- W2078303591 created "2016-06-24" @default.
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- W2078303591 date "2011-03-01" @default.
- W2078303591 modified "2023-10-12" @default.
- W2078303591 title "Cofiniteness of extension functors of cofinite modules" @default.
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- W2078303591 doi "https://doi.org/10.1016/j.jalgebra.2010.11.016" @default.
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