  As well-known, in a finitary algebraic structure the set $\Gamma$ of all the
non-generators is the intersection of all the maximal proper substructures. In
particular, $\Gamma$ is a substructure.
  We show that the corresponding statements hold for complete semilattices but
fail for complete lattices, when as the notion of substructure we take complete
subsemilattices and complete sublattices, respectively.
