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In this paper, we find necessary and sufficient condition for the existence of amenable traces on the reduced semigroup CÃ¢??-algebra of a cancellative semigroup. As an application, we give conditions for the reduced semigroup CÃ¢??-algebra of a left Ore semigroup to be quasidiagonal (QD). We also find conditions under which this CÃ¢??-algebra is a matricial field (MF) or residually finite dimensional (RFD). Some illustrative examples are provided.
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