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.
Categories: math.OA