  We reinvestigate Kreimer's Hopf algebra structure of perturbative quantum
field theories with a special emphasis on overlapping divergences. Kreimer
first disentangles overlapping divergences into a linear combination of
disjoint and nested ones and then tackles that linear combination by the Hopf
algebra operations. We present a formulation where the Hopf algebra operations
are directly defined on any type of divergence. We explain the precise relation
to Kreimer's Hopf algebra and obtain thereby a characterization of their
primitive elements.
