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Vietnam Journal of Mathematics 40:4(2012)
497-503
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On the Regularity of Generalized Local Cohomology
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Naser Zamani
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Faculty
of Science, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
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Received October 13,
2011
Revised April 3, 2012
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Abstract. Let $R=\oplus_{j\geq 0}R_j$ be a
positively graded Noetherian ring with local base ring $(R_0,\frak{m}_0)$
and the irrelevant ideal $R_+=\oplus_{j\geq 1}R_j$. Let M, N be two finitely generated graded R-modules with pd(M)
< ∞. The vanishing of homogeneous components of generalized local
cohomology modules with support in different graded ideals in a certain
graded ring will be compared and using the result a bound for the
regularity of the pair (M, N) relative to the graded ideal
$\frak{a}\supseteq R_+$ will be obtained.
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2000 Mathematics
Subject Classification. 13D45, 13E10.
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Keywords.
Generalized local cohomology, regularity.
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Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by Springer
since January 2013
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