2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/81724Basic idea presented in Parts (I) and (II) for the deformed boson scheme is applied to the case of the su(2,1)-algebra for describing many-body systems consisting of three kinds of boson operators. A possible form of the coherent state for the su(2,1)-algebra is generalized and the deformed su(2,1)-algebra is presented. As an application, the time-evolution of the statistically mixed state in a certain boson system, which has been already investigated by the present authors, is reinvestigated.24 pages, no figure, using PTPTeX styleNuclear Theorytext