THE HOPF RING FOR P(N)

We show that E(P(n)*), the E-homology of the Omega-spectrum for P(n), is an E free Hopf ring for E a complex oriented theory with I-n sent to 0. This covers the cases P(q)(P(n)*) and K(q)*(P(n)*), q greater than or equal to n. The generators of the Hopf ring are those necessar y for the stable result. The motivation for this paper is to show that P(n) satisfies all of the conditions for the machinery of unstable co homology operations set up in [BJW95]. This can then be used to produc e splittings analogous to those for BP done in [Wil75].