%0 Journal Article %T ARTINIANNESS OF COMPOSED LOCAL COHOMOLOGY MODULES %J Journal of Algebraic Systems %I Shahrood University of Technology %Z 2345-5128 %A Saremi, H. %D 2016 %\ 09/01/2016 %V 4 %N 1 %P 79-84 %! ARTINIANNESS OF COMPOSED LOCAL COHOMOLOGY MODULES %K Generalized local cohomology %K Local cohomology %K Artinian modules %R 10.22044/jas.2016.730 %X Let $R$ be a commutative Noetherian ring and let $fa$, $fb$ be two ideals of $R$ such that $R/({fa+fb})$ is Artinian. Let $M$, $N$ be two finitely generated $R$-modules. We prove that $H_{fb}^j(H_{fa}^t(M,N))$ is Artinian for $j=0,1$, where $t=inf{iin{mathbb{N}_0}: H_{fa}^i(M,N)$ is not finitelygenerated $}$. Also, we prove that if $DimSupp(H_{fa}^i(M,N))leq 2$, then $H_{fb}^1(H_{fa}^i(M,N))$ is Artinian for all $i$. Moreover, we show that if $dim N=d$, then $H_{fb}^j(H_{fa}^{d-1}(N))$ is Artinian for all $jgeq 1$. %U https://jas.shahroodut.ac.ir/article_730_b73d8831c14ac1772432c3f6a0548594.pdf