This paper continues the study
of how the ideal structure of a Chevalley algebra (a Lie algebra obtained by
transferring the scalars of a finite dimensional simple Lie algebra over C to a
commutative ring R with identity in which 2 and 3 are not zero divisors) depends on
the ideal structure of R. Specifically, we find that composition series of ideals for the
Chevalley algebras exist only in case R has composition series of ideals,
and in the latter case give explicit descriptions of the composition series in
the Chevalley algebras. We also give a necessary and sufficient condition
for the composition series in the algebra to exactly parallel those in the
ring.
