  It is shown that any generalized Kac-Moody Lie algebra g that has no mutually
orthogonal imaginary simple roots can be written as the vector space direct sum
of a Kac-Moody subalgebra and subalgebras isomorphic to free Lie algebras over
certain modules for the Kac-Moody subalgebra. Also included is a detailed
discussion of Borcherds' construction of the Monster Lie algebra from a vertex
algebra and an elementary proof of Borcherds' theorem relating Lie algebras
with `an almost positive definite bilinear form' to generalized Kac-Moody
algebras. (Preprint version 1996)
