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Properly separable mixed abelian groups A which are projective, respectively flat, as modules over their endomorphism rings are completely characterized. These results generalize the works of F. Richman and E. A. Walker. A subclass of separable mixed abelian groups-the properly separable groups-in which finitely many rank one summands can be embedded in a finite rank summand is considered here. It is shown that a reduced properly separable mixed abelian group A is projective as a module overdoi:10.1090/s0002-9939-1984-0740169-3 fatcat:atk245i5w5fjpgofgw6a3an33a