The paper deals with the computation of flows in coloured nets and with the potential reachability of markings over the integers in p/t nets. We introduce Artin nets as a subclass of coloured nets, which can be handled by methods from Commutative Algebra. As a first result we develop an algorithm for the explicit computation of flows in Artin nets, which is supported by existing tools. Concerning reachability in p/t nets we prove a refined rank condition as a second result.