Dehghani-Zadeh, F. (2020). Finiteness of certain local cohomology modules. Algebraic Structures and Their Applications, 7(1), 29-40. doi: 10.29252/as.2020.1683
Fatemeh Dehghani-Zadeh. "Finiteness of certain local cohomology modules". Algebraic Structures and Their Applications, 7, 1, 2020, 29-40. doi: 10.29252/as.2020.1683
Dehghani-Zadeh, F. (2020). 'Finiteness of certain local cohomology modules', Algebraic Structures and Their Applications, 7(1), pp. 29-40. doi: 10.29252/as.2020.1683
Dehghani-Zadeh, F. Finiteness of certain local cohomology modules. Algebraic Structures and Their Applications, 2020; 7(1): 29-40. doi: 10.29252/as.2020.1683
Department of mathematics, Islamic Azad University Yazd Branch, Yazd, Iran.
Abstract
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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