Iranian Journal of

Let $(R,fm,k)$ be a local Gorenstein ring of dimension $n$. Let $H_{I,J}^i(R)$ be the  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 the  dimension of $H_{I,J}^i(R)$.