Abstract
Let (R;m;k) be a local Gorenstein ring of dimension n. Let H i (R) be the local cohomology with respect to a pair of ideals I;J and c be the inffijH i (R) 6 0g. A pair of ideals I;J is called co- homologically complete intersection if H i (R) = 0 for all i 6 c. It is shown that, when H i (R) = 0 for all i 6 c, (i) a minimal injec- tive resolution of H c (R) presents like that of a Gorenstein ring; (ii) Hom R(H c (R); H c (R))' R, where (R;m) is a complete ring. Also we get an estimate of the dimension of H i (R).
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