TY - JOUR JF - IJMSI JO - IJMSI VL - 9 IS - 2 PY - 2014 Y1 - 2014/11/01 TI - Local Cohomology with Respect to a Cohomologically Complete Intersection Pair of Ideals TT - N2 - Let $(R,fm,k)$ be a local Gorenstein ring of dimension $n$. Let $H_{I,J}^i(R)$ be theĀ  local cohomology with respect to a pair of ideals $I,J$ and $c$ be the $inf{i|H_{I,J}^i(R)neq0}$. A pair of ideals $I, J$ is called cohomologically complete intersection if $H_{I,J}^i(R)=0$ for all $ineq c$. It is shown that, when $H_{I,J}^i(R)=0$ for all $ineq c$, (i) a minimal injective resolution of $H_{I,J}^c(R)$ presents like that of a Gorenstein ring (ii) $Hom_R(H_{I,J}^c(R),H_{I,J}^c(R))simeq R$, where $(R,fm)$ is a complete ring. Also we get an estimate of theĀ  dimension of $H_{I,J}^i(R)$. SP - 7 EP - 13 AU - Pour Eshmanan Talemi, A. AU - Tehranian, A. AD - KW - Vanishing KW - Local cohomology KW - Gorenstein ring. UR - http://ijmsi.ir/article-1-640-en.html DO - 10.7508/ijmsi.2014.02.002 ER -