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# Cofiniteness of Generalized Local Cohomology Modules for One-Dimensional Ideals

Published:2011-03-21
Printed: Mar 2012
• Kamran Divaani-Aazar,
Department of Mathematics, Az-Zahra University, Vanak, Post Code 19834, Tehran, Iran
• Alireza Hajikarimi,
Science and Research Branch, Islamic Azad University, Tehran, Iran
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## Abstract

Let $\mathfrak a$ be an ideal of a commutative Noetherian ring $R$ and $M$ and $N$ two finitely generated $R$-modules. Our main result asserts that if $\dim R/\mathfrak a\leq 1$, then all generalized local cohomology modules $H^i_{\mathfrak a}(M,N)$ are $\mathfrak a$-cofinite.
 Keywords: cofinite modules, generalized local cohomology modules, local cohomology modules
 MSC Classifications: 13D45 - Local cohomology [See also 14B15] 13E05 - Noetherian rings and modules 13E10 - Artinian rings and modules, finite-dimensional algebras