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.

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