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We study a class of stably projectionless simple C*-algebras which may beviewed as having generalized tracial rank one in analogy with the unital case.Some structural question concerning these simple C*-algebras are studied. Thepaper also serves as a technical support for the classification of separablestably projectionless simple amenable Jiang-Su stable C*-algebras.

Simple stably projectionless C*-algebras with generalized tracial rank one