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Cancellation Does not Imply Stable Rank One
Author(s) -
Toms Andrew S.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609306018807
Subject(s) - mathematics , rank (graph theory) , combinatorics
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. 2000 Mathematics Subject Classification 46L80 (primary), 46L85 (secondary).