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On the asymptotic behaviour of graded generalized local cohomology modules

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Author(s): F. Dehghani-Zadeh

Journal: Mathematical Sciences Quarterly Journal
ISSN 2008-1359

Volume: 5;
Issue: 1;
Start page: 13;
Date: 2011;
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Keywords: Associated primes | Asymptotic behaviours | Graded generalized local cohomology | Tameness.

ABSTRACT
Let ${R=igoplus_{ngeq 0}R_n}$ be a graded Noetherian ring withlocal base ring $R_0$ and let ${R_{+}=igoplus_{ngeq 1}R_n}$.Let $M$ and $N$ be finitely generated graded $R$-modules. In thispaper, we prove some results on the asymptotic behaviour of the$n$-th graded components $H^i_{R_+}(M,N)_{n}$ of $H^i_{R_+}(M,N)$for $no-infty$. We also study the tameness and asymptoticalstability of the homogeneous components of $H_{R_{+}}^{i}(M, N)$for some $i^{,}s$ with a specified property.
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