We show that every separable $C^$-algebra of real rank zero tensorially absorbs the Jiang–Su algebra contains a dense set generators. It follows that, in classifiable, simple, nuclear $C^$-algebra, generic element is generator.

We present the first range result for the total K-theory of C∗-algebras. This invariant has been used successfully to classify certain separable, nuclear C∗-algebras of real rank zero. Our results complete the classification of the so-called AD algebras of real rank zero.

We prove that a crossed product algebra arising from a minimal dynamical system on the product of the Cantor set and the circle has real rank zero if and only if that system is rigid. In the case that cocycles take values in the rotation group, it is also shown that rigidity implies tracial rank zero, and in particular, the crossed product algebra is isomorphic to a unital simple AT-algebra of ...