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46l85 (secondary)

Bulletin of the London Mathematical Society (1)

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CANCELLATION DOES NOT IMPLY STABLE RANK ONE
ANDREW S. TOMS
Journal:

Bulletin of the London Mathematical Society / Volume 38 / Issue 6 / December 2006

Published online by Cambridge University Press:

19 December 2006, pp. 1005-1008

Print publication:

December 2006
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A unital C*-algebra $A$ is said to have cancellation of projections if the semigroup $D(A)$ of Murray–von Neumann equivalence classes of projections in matrices over $A$ is cancellative. It has long been known that stable rank one implies cancellation for any $A$, and some partial converses have been established. In this paper it is proved that cancellation does not imply stable rank one for simple, stably finite C*-algebras.