Document Type : Original Manuscript


1 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.

2 Department of Mathematics, University of Payame Noor, P.O.Box 19395-3697, Tehran, Iran.


Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standard
graded ring, $M$ be a finitely generated graded $R$-module and $J$
be a homogenous ideal of $R$. In this paper we study the graded
structure of the $i$-th local cohomology module of $M$ defined by a
pair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. More
precisely, we discuss finiteness property and vanishing of the
graded components $H^{i}_{R_{+},J}(M)_{n}$.

Also, we study the Artinian property and tameness of certain
submodules and quotient modules of $H^{i}_{R_{+},J}(M)$.