  An ideal I of a local Cohen-Macaulay ring R is called a cohomologically
complete intersection if H^i_I(R) = 0 for all i \neq c = height(I). Here
H^i_I(R), i \in Z denotes the local cohomology of R with respect to I. For
instance, a set-theoretic complete intersection is a cohomologically complete
intersection. Here we study cohomologically complete intersections from various
homological points of view. As a main result it is shown that the vanishing
H^iI_(M) = 0 for all i \neq c is completely encoded in homological properties
of H^cI_(M). These results extend those of Hellus and Schenzel (see [13,
Theorem 0.1]) shown in the case of a local Gorenstein ring. In particular we
get a characterization of cohomologically complete intersections in a
Cohen-Macaulay ring in terms of the canonical module.
