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March 28, 2026

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

Key Points

To explore the relationships between implicative homomorphisms and ternary semigroup homomorphisms in implicative n.p.o. ternary semigroups.
Review of existing literature on implicative n.p.o. semigroups and their homomorphisms.
Theoretical analysis of the properties of ternary semigroups and implicative structures.
Establishment of connections between various homomorphisms in the context of n.p.o. semigroups.
Increased understanding of implicative homomorphisms in the framework of ternary semigroups.
Defined new relationships between homomorphisms that are specific to negatively partially ordered structures.

Abstract

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.

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