Strict comparison and Z-absorption of nuclear C*-algebras
  For any unital separable simple infinite-dimensional nuclear C*-algebra with finitely many extremal traces, we prove that Z-absorption, strict comparison, and property (SI) are equivalent. We also show that any unital separable simple nuclear C*-algebra with tracial rank zero is approximately divisible, and hence is Z-absorbing. 
Hiroki Matui, Yasuhiko Sato
math.OA