IJPAM: Volume 69, No. 4 (2011)

SOME RESULTS ON GRADED GENERALIZED
LOCAL COHOMOLOGY MODULES

F. Dehghanizadeh$^1$, H. Zakeri$^2$
$^1$Department of Mathematics
Science and Research Campus
Islamic Azad University
Tehran, IRAN
e-mail: f.dehghanizadeh@yahoo.com
$^2$faculty of Mathematics and Computer Science
Tarbiat Moallem University
Tehran, 15618, IRAN


Abstract. Let $R=\op_{n\geq 0}R_n$ be a graded Noetherian ring with local base ring $R_0$ and let $R_+=\op_{n\geq 1}R_n$. Let $M$ and $N$ be finitely generated graded $R$-modules. In this paper we extend some of the known results about ordinary local cohomology modules $H^i_{R_+}(M)$ to generalized local cohomology modules $H^i_{R_+}(M,N)$. Indeed, among other things, we prove that certain submodules and factor modules of $H^i_{R_+}(M,N)$ are Artinian for some $i$. Also we obtain 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 $n\lo-\infty$.

Received: December 20, 2010

AMS Subject Classification: 13D45, 13E10, 13A02

Key Words and Phrases: associated primes, asymptotic behaviour, generalized local cohomology, graded components

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 4