  We calculate the real rank and stable rank of CCR algebras which either have
only finite dimensional irreducible representations or have finite topological
dimension. We show that either rank of A is determined in a good way by the
ranks of an ideal I and the quotient A/I in four cases: When A is CCR; when I
has only finite dimensional irreducible representations; when I is separable,
of generalized continuous trace and finite topological dimension, and all
irreducible representations of I are infinite dimensional; or when I is
separable, stable, has an approximate identity consisting of projections, and
has the corona factorization property. We also present a counterexample on
higher ranks of M(A), A subhomogeneous, and a theorem of P. Green on
generalized continuous trace algebras.
