Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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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.

Finiteness properties generalized local cohomology with respect to an ideal containing the irrelevant ideal

Fatemeh Dehghani-Zadeh

Islamic Azad University

Abstract

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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