  Let A be a unital separable simple C*-algebra with a unique tracial state. We
prove that if A is nuclear and quasidiagonal, then A tensored with the
universal UHF-algebra has decomposition rank at most one. Then it is proved
that A is nuclear, quasidiagonal and has strict comparison if and only if A has
finite decomposition rank. For such A, we also give a direct proof that A
tensored with a UHF-algebra has tracial rank zero. Applying this
characterization, we obtain a counter-example to the Powers-Sakai conjecture.

Operator Algebras