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Journals / Turkish Journal of Mathematics and Computer Science / 2020 / Cilt: 12 Sayı: 1

Semilattice Co-Congruence in $\Gamma$-Semigroups

Daniel A. ROMANO
Pages
1–7
Publication Date
2020-06-29
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Additionally, it is investigated (co-ordered) semilattice co-congruence on (co-ordered) $\Gamma$-semigroup with apartness.

📌 3 Key Takeaways

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Objective & Hypothesis:As a generalization of semigroups, Sen, in 1981, introduced the concept of $\Gamma$-semigroups.
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Key Findings & Data:Soc.}, 34(1)(2019), 71--83.) it is introduced and analyzed the concept of $\Gamma$-semigroups with apartness in Bishop's constructive framework.
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Conclusion & Impact:Additionally, it is investigated (co-ordered) semilattice co-congruence on (co-ordered) $\Gamma$-semigroup with apartness.
🔬Design:Research Article
📍Scope:2019 Verileri
⚙️Variables:Bishop’s constructive algebra · Intuitionistic logic · $\Gamma$-semigroup with apartness

Abstract

As a generalization of semigroups, Sen, in 1981, introduced the concept of $\Gamma$-semigroups. In the author's paper (D A. Romano. $\Gamma$-semigroups with apartness. \emph{Bull. Allahabad Math. Soc.}, 34(1)(2019), 71--83.) it is introduced and analyzed the concept of $\Gamma$-semigroups with apartness in Bishop's constructive framework. In this article, as a continuation of previous research, the concept of co-congruences in $\Gamma$-semigroups is introduced and analyzed. Additionally, it is investigated (co-ordered) semilattice co-congruence on (co-ordered) $\Gamma$-semigroup with apartness.

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Cite This Article

ROMANO, D. A. (2020). Semilattice Co-Congruence in $\Gamma$-Semigroups. Turkish Journal of Mathematics and Computer Science, Cilt: 12 Sayı: 1, 1–7. https://ajindex.com/articles/934321

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References (5)

  1. Bishop, E., Foundations of Constructive Analysis, New York: McGraw-Hill, 1967.
  2. Bridges, D. S., Richman, F., Varieties of Constructive Mathematics, Cambridge: London Mathematical Society Lecture Notes, No. 97, Cambridge University Press, 1987.
  3. Cherubini, A., Frigeri, A., \emph{Inverse semigroups with apartness}, Semigroup Forum, \textbf{98}(3)(2019), 571--588. Crvenkovi\'c, S., Mitrovi\'c, M., Romano, D. A., \emph{Semigroups with apartness}, Math. Logic Quarterly, \textbf{59}(6)(2013), 407--414. Crvenkovi\'c, S., Mitrovi\'c, M., Romano, D. A., \emph{Basic notions of (Constructive) semigroups with apartness}, Semigroup Forum, \textbf{92}(3)(2016), 659--674. Hedayati, H., \emph{Isomorphisms via congruences on $\Gamma$-semigroups and $\Gamma$-ideals}, Thai J. Math., \textbf{11}(3)(2013), 563--575. Kehayopulu, N., \emph{On ordered $\Gamma$-semigroups}, Sci. Math. Japonicae Online, \textbf{e-2010}, 37--43. Kwon, Y. I., Li, S. K., \emph{Some special elements in ordered $\Gamma$-semigroups}. Kyungpook Math. J., \textbf{35}(3)(1996), 679--685. Mines, R., Richman, F., Ruitenburg, W., A course of constructive algebra, Springer-Verlag, New York 1988.
  4. Romano, D. A., \emph{Coequality relations, a survey}, Bull. Soc. Math. Banja Luka, \textbf{3}(1996), 1--36. Romano, D. A., \emph{Co-ideals and co-filters in ordered set under co-quasiorder}, Bull. Int. Math. Virtual Inst., \textbf{8}(1)(2018), 177--188. Romano, D. A., \emph{$\Gamma$-semigroups with apartness}, Bull. Allahabad Math. Soc., \textbf{34}(1)(2019), 71--83. Romano, D. A., \emph{Some algebraic structures with apartness. A review}, J. Int. Math. Virtual Inst., \textbf{9}(2)(2019), 361--395. Romano, D. A., \emph{On coequality relation on set with apartness}, Bull. Int. Math. Virtual Inst., \textbf{9}(1)(2019), 1--9. Romano, D. A., \emph{Co-filters in $\Gamma$-semigroups ordered under co-order}, (To appear) Available at ResearchGate Sen, M. K., \emph{On $\Gamma$-semigroups}. In: Proceeding of International Conference on 'Algebra and its Applications,(New Delhi, 1981)' (pp. 301--308). Lecture Notes in Pure and Appl. Math. 9, New York: Decker Publication, 1984.
  5. Sen, M. K., Saha, N. K., \emph{On $\Gamma$-semigroup, I}, Bull. Calcutta Math. Soc., \textbf{78}(1986), 181--186. Seth, A. \emph{$\Gamma$-group congruence on regular $\Gamma$-semigroups}. Inter. J. Math. Math. Sci., \textbf{15}(1)(1992), 103--106. Siripitukdet, M., Iampan, A., \emph{On the least (ordered) semilattice congruence in ordered $\Gamma$-semigroups},