  We prove generalized lower Ricci bounds for Euclidean and spherical cones
over complete Riemannian manifolds. These cones are regarded as complete metric
measure spaces. In general, they will be neither manifolds nor Alexandrov
spaces. We show that the Euclidean cone over an n-dimensional Riemannian
manifold whose Ricci curvature is bounded from below by n-1 satisfies the
curvature-dimension condition CD(0; n+1) and that the spherical cone over the
same manifold fulfills the curvature-dimension condition CD(n; n+1). More
generally, for each N > 1 we prove that the condition CD(N-1;N) for a weighted
Riemannian space is equivalent to the condition CD(0;N +1) for its N-Euclidean
cone as well as to the condition CD(N;N + 1) for its N-spherical cone.
