  The main result here is that a simple separable C*-algebra is Z-stable (where
Z denotes the Jiang-Su algebra) if (i) it has finite nuclear dimension or (ii)
it is approximately subhomogeneous with slow dimension growth. This generalizes
the main results of [Toms, "K-theoretic rigidity and slow dimension growth";
Winter, "Nuclear dimension and Z-stability of pure C*-algebras"] to the
nonunital setting. As a consequence, finite nuclear dimension implies
Z-stability even in the case of a separable C*-algebra with finitely many
ideals. Algebraic simplicity is established as a fruitful weakening of being
simple and unital, and the proof of the main result makes heavy use of this
concept.
