ON GRADED LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS

Authors

  • Maryam Jahangiri Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran AND Institute for Research in Fundamental Sciences (IPM) P.O.Box: 19395- 5746, Tehran, Iran.
  • Zohreh Habibbi Department of Mathematics, University of Payame Noor, P.O.Box 19395-3697, Tehran, Iran.
Abstract:

Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standardgraded ring, $M$ be a finitely generated graded $R$-module and $J$be a homogenous ideal of $R$. In this paper we study the gradedstructure of the $i$-th local cohomology module of $M$ defined by apair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. Moreprecisely, we discuss finiteness property and vanishing of thegraded components $H^{i}_{R_{+},J}(M)_{n}$.Also, we study the Artinian property and tameness of certainsubmodules and quotient modules of $H^{i}_{R_{+},J}(M)$.

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Journal title

volume 3  issue 2

pages  133- 146

publication date 2015-01-01

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