Finiteness of certain local cohomology modules

Document Type : Research Paper


Department of mathematics, Islamic Azad University Yazd Branch, Yazd, Iran.



Cofiniteness of the generalized local cohomology modules
$H^{i}_{\mathfrak{a}}(M,N)$ of two $R$-modules $M$ and $N$ with
respect to an ideal $\mathfrak{a}$ is studied for some $i^{,}s$ with
a specified property. Furthermore, Artinianness of
$H^{j}_{\mathfrak{b}_{0}}(H_{\mathfrak{a}}^{i}(M,N))$ is
investigated by using the above result, in certain graded situations, where $\mathfrak{b}_{0}$ is an ideal of $R_{0}$ and
$\mathfrak{a}=\mathfrak{a}_{0}+R_{+}$ such that
$\mathfrak{b}_{0}+\mathfrak{a}_{0}$ is an  $\mathfrak{m}_{0}$-primary ideal.


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