Integrating Hasse–Schmidt derivations

We study integrating (that is expanding to a Hasse–Schmidt derivation) derivations, and more generally truncated Hasse–Schmidt derivations, satisfying iterativity conditions given by formal group laws. Our results concern the cases of the additive and the multiplicative group laws. We generalize a theorem of Matsumura about integrating nilpotent derivations (such a generalization is implicit in work of Ziegler) and we also generalize a theorem of Tyc about integrating idempotent derivations.