Geodesic
C* -Algebras of Real Rank Zero Whose K0's are not Riesz Groups
Canadian mathematical bulletin, Tome 39 (1996) no. 4, pp. 429-437

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DOI

Examples are constructed of stably finite, imitai, separable C* -algebras A of real rank zero such that the partially ordered abelian groups K0(A) do not satisfy the Riesz decomposition property. This contrasts with the result of Zhang that projections in C* -algebras of real rank zero satisfy Riesz decomposition. The construction method also produces a stably finite, unital, separable C* -algebra of real rank zero which has the same K-theory as an approximately finite dimensional C*-algebra, but is not itself approximately finite dimensional.
DOI : 10.4153/CMB-1996-051-2
Mots-clés : 46L80, 19K14 
Goodearl, K. R. C* -Algebras of Real Rank Zero Whose K0's are not Riesz Groups. Canadian mathematical bulletin, Tome 39 (1996) no. 4, pp. 429-437. doi: 10.4153/CMB-1996-051-2
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     author = {Goodearl, K. R.},
     title = {C* {-Algebras} of {Real} {Rank} {Zero} {Whose} {K0's} are not {Riesz} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {429--437},
     year = {1996},
     volume = {39},
     number = {4},
     doi = {10.4153/CMB-1996-051-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-051-2/}
}
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