%0 Journal Article %T On the cofiniteness of local cohomology modules %J Algebraic Structures and Their Applications %I Yazd University %Z 2382-9761 %A Roshan-Shekalgourabi, Hajar %D 2022 %\ 02/01/2022 %V 9 %N 1 %P 81-92 %! On the cofiniteness of local cohomology modules %K local cohomology modules %K $I$-cofinite modules %K Minimax modules %K Weakly Laskerian modules %K Krull dimension %K Bass numbers %R 10.22034/as.2021.2382 %X 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 $\dim H^i_I(M)\leq 1$ for all $i$, then for any $i \geq 0$ 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 [8, Theorem 2.6]. As a consequence, the Bass numbers and Betti numbers of $H^i_I (M)$ are finite for all $i \geq 0$. Also, among other things, we show that if either $\dim R/I\leq 2$ or $\dim M\leq 2$, 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 $i \geq 0$ and $j\geq 0$. This generalizes [1, Corollary 2.8]. %U https://as.yazd.ac.ir/article_2382_54f960a8c580354b018d44d0d40bf970.pdf