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Relevant bibliographies by topics / Commutative Ordered Ternary Semigroup

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Academic literature on the topic 'Commutative Ordered Ternary Semigroup'

Author: Grafiati

Published: 7 June 2025

Last updated: 17 July 2025

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Journal articles on the topic "Commutative Ordered Ternary Semigroup"

1

Nakwan, Kansada, Panuwat Luangchaisri, and Thawhat Changphas. "Implicative Negatively Partially Ordered Ternary Semigroups." European Journal of Pure and Applied Mathematics 17, no. 4 (2024): 4180–94. https://doi.org/10.29020/nybg.ejpam.v17i4.5511.

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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 implicativehomomorphism 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

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2

Shinde, Dattatray N., Machchhindra T. Gophane, and Manish C. Agalave. "Ordered Pseudo-Ideals of An Ordered Ternary Semigroup." Indian Journal Of Science And Technology 18, no. 4 (2025): 281–86. https://doi.org/10.17485/ijst/v18i4.3500.

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Objectives: This research explores the concept of ordered pseudo-ideals in an ordered ternary semigroup 𝐺, which builds on the existing idea of pseudoideals in a semigroup. Methods: The investigation delves into some unique properties of ordered pseudo-ideals in an ordered ternary semigroup 𝐺. Findings: This study has established many sufficient conditions for (𝐿𝑀𝑁] to be an ordered pseudo-ideal of 𝐺 where 𝐿, 𝑀 and 𝑁 are non-empty subsets of 𝐺. Additionally, the study provides conditions for subsets (𝐿𝐵𝐵] and (𝐵𝐵𝐿] to be recognized as ordered left and right pseudo-ideals, respectively, as well

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3

Dattatray, N. Shinde, T. Gophane Machchhindra, and C. Agalave Manish. "Ordered Pseudo-Ideals of An Ordered Ternary Semigroup." Indian Journal of Science and Technology 18, no. 4 (2025): 281–86. https://doi.org/10.17485/IJST/v18i4.3500.

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<strong>Objectives:</strong> This research explores the concept of ordered pseudo-ideals in an ordered ternary semigroup 𝐺, which builds on the existing idea of pseudoideals in a semigroup. <strong>Methods:</strong> The investigation delves into some unique properties of ordered pseudo-ideals in an ordered ternary semigroup 𝐺. <strong>Findings:</strong> This study has established many sufficient conditions for (𝐿𝑀𝑁] to be an ordered pseudo-ideal of 𝐺 where 𝐿, 𝑀 and 𝑁 are non-empty subsets of 𝐺. Additionally, the study provides conditions for subsets (𝐿𝐵𝐵] and (𝐵𝐵𝐿] to

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4

Gophane, Machchhindra T., and Dattatray N. Shinde. "MAXIMAL AND MINIMAL PSEUDO SYMMETRIC IDEALS IN PARTIALLY ORDERED TERNARY SEMIGROUPS." South East Asian Journal of Mathematics and Mathematical Sciences 20, no. 02 (2024): 121–32. https://doi.org/10.56827/seajmms.2024.2002.9.

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We have introduced the notions of maximal and minimal pseudo symmetric ideals of a partially ordered ternary semigroup $T$ and studied their properties. We show that every maximal pseudo symmetric ideal of a commutative partially ordered ternary semigroup with identity is a prime pseudo symmetric ideal. We gave an example to show that the converse of this statement is not true.

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5

Nakwan, Kansada, Panuwat Luangchaisri, and Thawhat Changphas. "On Filters of Implicative Negatively Partially Ordered Ternary Semigroups." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5859. https://doi.org/10.29020/nybg.ejpam.v18i2.5859.

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In this paper, we study a special set in an implicative n.p.o.(negatively partially ordered) ternary semigroup, and prove that a filter can be represented by the union of such sets. Indeed, let $(T, [\,\,\,],\leq,[\,\,\,]^*)$ be an implicative n.p.o. ternary semigroup. For any $a, b\in T$, we define $$S(a,b):=\{c\in T \,:\, [aa[bbc]^*]^*=1\}.$$ We have the following:\begin{enumerate} \item [(1)] A non-empty subset $F$ of $T$ isa filter if and only if it satisfies the following conditions: \begin{enumerate} \item[(F3)] $1\in F$; \item[(F4)] for any $a, b,c \in T$, if $[abc]^*\in F$ and $a,b \in

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6

G, Ramesh, and Mahendran S. "Some Properties of Commutative Ternary Right Almost Semigroups." Indian Journal of Science and Technology 16, no. 45 (2023): 4255–66. https://doi.org/10.17485/IJST/v16i45.1937.

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Abstract <strong>Objective/Background:</strong> In this paper, the concept of commutative ternary right almost semigroups is introduced. The properties of ternary right almost semigroups and commutative ternary right almost semigroups are also discussed. Finally, regular only and the regularity are also explored in ternary right almost semigroups. <strong>Methods:</strong> Properties of ternary right almost semigroup have been employed to carry out this research work to obtain all the characterizations of commutative ternary right almost semigroups, regular and normal correspond

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7

Jantanan, Wichayaporn, Natee Raikham, and Ronnason Chinram. "On right bases of partially ordered ternary semigroups." Quasigroups and Related Systems 30, no. 2(48) (2023): 209–18. http://dx.doi.org/10.56415/qrs.v30.18.

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We investigate the results of a partially ordered ternary semigroup containing right bases and characterize when a non-empty subset of a partially ordered ternary semigroup is a right base. Moreover, we give a characterization of a right base of a partially ordered ternary semigroup to be a ternary subsemigroup and we show that the right bases of a partially ordered ternary semigroup have same cardinality. Finally, we show that the complement of the union of all right bases of a partially ordered ternary semigroup is a maximal proper left ideal.

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8

Andri, Andri, and Nasria Nacong. "KONDISI MINIMAL IDEAL KIRI TERURUT PADA SEMIGRUP TERNER TERURUT PARSIAL." JURNAL ILMIAH MATEMATIKA DAN TERAPAN 15, no. 2 (2019): 280–87. http://dx.doi.org/10.22487/2540766x.2018.v15.i2.13225.

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Ternary semigroups 𝑇 is obtained from a nonempty set 𝑇 that given a mapping with a multiplication operation ternary that satisfied closed and associative properties. So, generally a ternary semigroup is an abstraction of a semigroup structure. Meanwhile, partially ordered ternary semigroups 𝑇 is an ordered semigroup 𝑇 that satisfies the properties for each 𝑎, 𝑏, 𝑐, 𝑑 ∈ 𝑇 if 𝑎 ≤ 𝑏 then (𝑎𝑐𝑑) ≤ (𝑏𝑐𝑑) and (𝑑𝑐𝑎) ≤ (𝑑𝑐𝑏). In a ternary semigroups there is also concept of left ideals. This study was conducted to examine the characteristics of ordered left ideals on partially ordered ternary semigroup

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9

Shinde, Dattatray, and Machchhindra Gophane. "On irreducible pseudo symmetric ideals of a partially ordered ternary semigroup." Quasigroups and Related Systems 30, no. 1(47) (2022): 169–80. http://dx.doi.org/10.56415/qrs.v30.15.

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In this paper, the concepts of irreducible and strongly irreducible pseudo symmetric ideals in a partially ordered ternary semigroup are introduced. We also studied some interesting properties of irreducible and strongly irreducible pseudo symmetric ideals of a partially ordered ternary semigroup and prove that the space of strongly irreducible pseudo symmetric ideals of a partially ordered ternary semigroup is topologized.

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10

Gophane, Machchhindra, and Dattatray Shinde. "On pseudo-ideals in partially ordered ternary semigroups." Quasigroups and Related Systems 32, no. 1(51) (2024): 41–48. https://doi.org/10.56415/qrs.v32.04.

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We study the properties of different types of pseudo-ideals of a partially ordered ternary semigroup and prove that the space of all strongly irreducible pseudoideals of a partially ordered ternary semigroup is a compact space.

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