  The main result of this paper is the construction of ``good'' integral forms
for the universal enveloping algebras of the fake monster Lie algebra and the
Virasoro algebra. As an application we construct formal group laws over the
integers for these Lie algebras. We also prove a form of the no-ghost theorem
over the integers, and use this to verify an assumption used in the proof of
the modular moonshine conjectures.
