# Journal of Operator Theory

Volume 67, Issue 2, Spring 2012 pp. 329-334.

On extensions of stably finite $C^*$-algebras**Authors**: Hongliang Yao

**Author institution:**School of Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

**Summary:**In this paper, we prove that for any $C^*$-algebra $A$ with an approximate unit of projections, there is a smallest ideal $I$ of $A$, in which quotient $A/I$ is stably finite. We give a sufficient condition and a necessary condition on which $I$ is the smallest ideal in this case for $A$ by $K$-theory.

**Keywords:**extension, stably finite $C^*$-algebra, index map

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