On the cofiniteness of local cohomology modules

Let R be a commutative Noetherian ring with identity, I be an ideal of R and M be an R-module such that Ext^j_R(R/I, M) is finitely generated for all j. We prove that if \dim H^i_I(M)\leq ۱ for all i, then for any i \geq ۰ and for any submodule N of H^i_I(M) that is either I-cofinite or minimax, the R-module H^i_I(M)/N is I-cofinite. This generalizes the main result of Bahmanpour and Naghipour [۸, Theorem ۲.۶]. As a consequence, the Bass numbers and Betti numbers of H^i_I (M) are finite for all i \geq ۰. Also, among other things, we show that if either \dim R/I\leq ۲ or \dim M\leq ۲, then for each finitely generated R-module N, the R-module Ext^j_R (N, H^i_I(M)) is I-weakly cofinite, for all i \geq ۰ and j\geq ۰. This generalizes [۱, Corollary ۲.۸].

کلیدواژه ها:

local cohomology modules ، I-cofinite modules ، Minimax modules ، Weakly Laskerian modules ، Krull dimension ، Bass numbers