Implicative Negatively Partially Ordered TernarySemigroups
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i4.5511Keywords:
Implicative semilattice, Implicative n.p.o. (negatively partially ordered) ternary semigroup , Implicative homomorphism, FilterAbstract
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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Copyright (c) 2024 Kansada Nakwan, Panuwat Luangchaisri, Thawhat Changphas
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