Implicative homomorphisms between implicative n.p.o. ternary semigroups

The concept of implicative n.p.o. (negatively partially ordered) ternary semigroups, which extends the concept of implicative n.p.o. semigroups introduced by M. W. Chan and K. P. Shum in their paper “Homomorphisms of Implicative Semigroups,” Semigroup Forum, 46 (1993), 7–15, was studied by K. Nakwan, P. Luangchaisri, and T. Changphas in their paper “Implicative Negatively Partially Ordered Ternary Semigroups,” European Journal of Pure and Applied Mathematics, 17(4) (2024), 4180–4194. In this paper, we continue the study of these ternary semigroups and establish a connection between implicative homomorphisms and ternary semigroup homomorphisms of implicative n.p.o. ternary semigroups.