Extremal richness of multiplier and corona algebras of simple C* -algebras with real rank zero

In this paper we investigate the extremal richness of the multiplier algebra M(A) and the corona algebra M(A)/A, for a simple C* -algebra A with real rank zero and stable rank one. We show that the space of extremal quasitraces and the scale of A contain enough information to determine whether M(A)/A is extremally rich. In detail, if the scale is finite, then M(A)/A is extremally rich. In important cases, and if the scale is not finite, extremal richness is characterized by a restrictive condition: the existence of only one infinite extremal quasitrace which is isolated in a convex sense.