SavedAdd your journal

Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 12 Issue: 1

Semilattice Co-Congruence in $\Gamma$-Semigroups

Daniel A. Romano(International Mathematical Virtual Institute)0000-0003-1148-3258
Pages
—
Publication Date
2020-06-29
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ 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

🎯
Objective & Hypothesis:As a generalization of semigroups, Sen, in 1981, introduced the concept of $\Gamma$-semigroups.
📊
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.
💡
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.

🔖

Cite This Article

Romano, D. A. (2020). Semilattice Co-Congruence in $\Gamma$-Semigroups. Turkish Journal of Mathematics and Computer Science, Volume: 12 Issue: 1. https://ajindex.com/articles/1324846

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (20)

  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.
  4. Crvenkovi\'c, S., Mitrovi\'c, M., Romano, D. A., \emph{Semigroups with apartness}, Math. Logic Quarterly, \textbf{59}(6)(2013), 407--414.
  5. 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.
  6. Hedayati, H., \emph{Isomorphisms via congruences on $\Gamma$-semigroups and $\Gamma$-ideals}, Thai J. Math., \textbf{11}(3)(2013), 563--575.
  7. Kehayopulu, N., \emph{On ordered $\Gamma$-semigroups}, Sci. Math. Japonicae Online, \textbf{e-2010}, 37--43.
  8. Kwon, Y. I., Li, S. K., \emph{Some special elements in ordered $\Gamma$-semigroups}. Kyungpook Math. J., \textbf{35}(3)(1996), 679--685.
  9. Mines, R., Richman, F., Ruitenburg, W., A course of constructive algebra, Springer-Verlag, New York 1988.
  10. Romano, D. A., \emph{Coequality relations, a survey}, Bull. Soc. Math. Banja Luka, \textbf{3}(1996), 1--36.
  11. 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.
  12. Romano, D. A., \emph{$\Gamma$-semigroups with apartness}, Bull. Allahabad Math. Soc., \textbf{34}(1)(2019), 71--83.
  13. Romano, D. A., \emph{Some algebraic structures with apartness. A review}, J. Int. Math. Virtual Inst., \textbf{9}(2)(2019), 361--395.
  14. Romano, D. A., \emph{On coequality relation on set with apartness}, Bull. Int. Math. Virtual Inst., \textbf{9}(1)(2019), 1--9.
  15. Romano, D. A., \emph{Co-filters in $\Gamma$-semigroups ordered under co-order}, (To appear) Available at ResearchGate
  16. 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.
  17. Sen, M. K., Saha, N. K., \emph{On $\Gamma$-semigroup, I}, Bull. Calcutta Math. Soc., \textbf{78}(1986), 181--186.
  18. Seth, A. \emph{$\Gamma$-group congruence on regular $\Gamma$-semigroups}. Inter. J. Math. Math. Sci., \textbf{15}(1)(1992), 103--106.
  19. Siripitukdet, M., Iampan, A., \emph{On the least (ordered) semilattice congruence in ordered $\Gamma$-semigroups}, Thai J. Math., \textbf{4}(2)(2006), 403--415.
  20. Troelstra, A. S., van Dalen, D., Constructivism in Mathematics: An Introduction, Amsterdam: North-Holland, 1988.