J. Korean Math. Soc. 2012; 49(6): 1215-1227
Printed November 1, 2012
https://doi.org/10.4134/JKMS.2012.49.6.1215
Copyright © The Korean Mathematical Society.
Fatemeh Dehghani-Zadeh
Islamic Azad University
The membership of the generalized local cohomology modules $H^{i}_{\mathfrak{a}}(M,N)$ of two $R$-modules $M$ and $N$ with respect to an ideal $\mathfrak{a}$ in certain Serre subcategories of the category of modules is studied from below $(i < t)$. Furthermore, the behaviour of the $n$th graded component $H_a^i(M, N)_n$ of the generalized local cohomology modules with respect to an ideal containing the irrelevant ideal as $n\to\infty$ is investigated by using the above result, in certain graded situations.
Keywords: generalized local cohomology, finiteness, Serre subcategories
MSC numbers: 13D45, 13D07
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