  This article aims at advancing the recently introduced exponential method for
renormalisation in perturbative quantum field theory. It is shown that this new
procedure provides a meaningful recursive scheme in the context of the
algebraic and group theoretical approach to renormalisation. In particular, we
describe in detail a Hopf algebraic formulation of Bogoliubov's classical
R-operation and counterterm recursion in the context of momentum subtraction
schemes. This approach allows us to propose an algebraic classification of
different subtraction schemes. Our results shed light on the peculiar algebraic
role played by the degrees of Taylor jet expansions, especially the notion of
minimal subtraction and oversubtractions.
