the artinian property of certain graded generalized local chohomology modules
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abstract
let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{r_+}(m,n))$ is artinian if and only if $h^{t+2}_{frak{m}_0r}(h^1_{r_+}(m,n))$ is artinian.
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Journal title:
bulletin of the iranian mathematical societyPublisher: iranian mathematical society (ims)
ISSN 1017-060X
volume 41
issue 2 2015
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