The main result of this note is the description of an arbitrary block ideal of a reduced universal enveloping algebra in the nilpotent case via induced modules. From this it is possible to derive a dimension formula for the corresponding Jacobson radical resp. the projective indecomposable module depending on a so-called admissible linear form of the underlying Lie algebra. Moreover, the structure of projective covers of one-dimensional modules is completely determined, and in the general case it is shown that the tensor product of the dual of a simple module with its projective cover is always the projective cover of the one-dimensional trivial module.