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Vietnam Journal of Mathematics 40:4(2012) 497-503

 

On the Regularity of Generalized Local Cohomology

Naser Zamani

Faculty of Science, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran

Received October 13, 2011

Revised April 3, 2012

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.

2000 Mathematics Subject Classification. 13D45, 13E10.

Keywords. Generalized local cohomology, regularity.

 

 

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