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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

Strict comparison and $ \mathcal{Z} $-absorption of nuclear C∗-algebras