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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 cofinite modules, generalized local cohomology modules, local cohomology modules
MSC Classifications: 13D45, 13E05, 13E10 show english descriptions Local cohomology [See also 14B15]
Noetherian rings and modules
Artinian rings and modules, finite-dimensional algebras
13D45 - Local cohomology [See also 14B15]
13E05 - Noetherian rings and modules
13E10 - Artinian rings and modules, finite-dimensional algebras
 

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