\title{The Hopf ring for $P(n)$}
\author{Douglas C. Ravenel
\thanks{Partially supported by the National Science Foundation}
\\University of Rochester\\Rochester, New York 14627\\
{\small drav@troi.cc.rochester.edu}
\and
W. Stephen Wilson
\\Johns Hopkins University\\Baltimore, Maryland 21218\\
{\small wsw@math.jhu.edu}}
\maketitle
\begin{abstract}
We show that $E_*(\pn{n}{*})$, 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 $P(q)_*(\pn{n}{*})$ and
$K(q)_*(\pn{n}{*})$, $q \geq n$.
The generators of the Hopf ring are those necessary 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 cohomology
operations set up in Boardman-Johnson-Wilson.
This can then be used
to produce splittings analogous to those
for $BP$.
\end{abstract}