Abstract. A simple C * -algebra is constructed for which the Murray-von Neumann equivalence classes of projections, with the usual addition-induced by addition of orthogonal projections-form the additive semigroup {0, 2, 3, . . . }.(This is a particularly simple instance of the phenomenon of perforation of the ordered K 0 -group, which has long been known in the commutative case-for instance, in the case of the four-sphere-and was recently observed by the second author in the case of a simple C * -algebra.)
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