THE STRUCTURE OF POSITIVE ELEMENTS FOR C-ASTERISK-ALGEBRAS WITH REAL RANK ZERO

In this paper we give a representation theorem for the Cuntz monoid S( A) of a sigma-unital C-aigebra A with real rank zero and stable rank one, which allows to prove several Riesz decomposition properties on t he monoid. As a consequence, it is proved that the comparability condi tions (FCQ), stable (FCQ) and (FCQ+) are equivalent for simple C-alge bras with real rank zero. It is also shown that the Grothendieck group K-0(A) of S(A) is a Riesz group, and lattice-ordered under some addi tional assumptions on A.