  In this work we consider the computation of Groebner bases of the steady
state ideal of reaction networks equipped with mass-action kinetics.
Specifically, we focus on the role of intermediate species and the relation
between the extended network (with intermediate species) and the core network
(without intermediate species).
  We show that a Groebner basis of the steady state ideal of the core network
always lifts to a Groebner basis of the steady state ideal of the extended
network by means of linear algebra, with a suitable choice of monomial order.
As illustrated with examples, this contributes to a substantial reduction of
the computation time, due mainly to the reduction in the number of variables
and polynomials. We further show that if the steady state ideal of the core
network is binomial, then so is the case for the extended network, as long as
an extra condition is fulfilled. For standard networks, this extra condition
can be visually explored from the network structure alone.
