Implicative Negatively Partially Ordered TernarySemigroups

Authors

  • Kansada Nakwan Khon Kaen University
  • Panuwat Luangchaisri Khon Kaen University
  • Thawhat Changphas Khon Kaen University

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5511

Keywords:

Implicative semilattice, Implicative n.p.o. (negatively partially ordered) ternary semigroup , Implicative homomorphism, Filter

Abstract

In this paper, we introduce and examine the notion of implicative negatively partially ordered ternary semigroups, for short implicative n.p.o. ternary semigroup, which include an element that serves as both the greatest element and the multiplicative identity. We study the notion of implicative homomorphisms between these ternary semigroups, and have that any implicative
homomorphism is a homomorphism. Let φ : T1→T2 be an implicative homomorphism from a commutative implicative n.p.o. ternary semigroup T1 onto T2. We construct a quotient commutative implicative n.p.o. ternary semigroup T1/ρKer φ, where ρKer φ is a congruence relation defined by Ker φ. We prove that there exists an implicative homomorphism ψ such that ψ ◦ η = φ, where η is a canonical homomorphism from T1 onto T1/ρKerφ.

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Published

2024-10-31

Issue

Section

Nonlinear Analysis

How to Cite

Implicative Negatively Partially Ordered TernarySemigroups. (2024). European Journal of Pure and Applied Mathematics, 17(4), 4180-4194. https://doi.org/10.29020/nybg.ejpam.v17i4.5511