A RATIONAL APPROACH TO HOPF RINGS

We study Hopf rings of the form E(F*), where E*(-) is a complex orien ted homology theory and F is the graded ring space arising from a com plex oriented Omega-spectrum F. We propose a new model Kopf ring E(Q) (F) which is constructed by purely algebraic means from the rationali sations EQ(F*), E*(FQ*) and EQ*(FQ*), and which in many cases is isom orphic to E(F*). Our model may be expressed in terms of the conjugate Bell polynomials associated with the exponential series for E and F, and we explain how calculations may be carried out in this context. We discuss the relationship between E(Q)(F*) and the well-known model E (R)(F*) due to Ravenel and Wilson.