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Journals / Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 23 Sayı: 1

Bruck-Reilly extension of a ternary monoid

Bir üçlü monoidin Bruck-Reilly genişlemesi

Seda Oğuz Ünal(SİVAS CUMHURİYET ÜNİVERSİTESİ)0000-0003-1338-1466
Pages
252–258
Publication Date
2021-01-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Additionally, some results about this construction are given which belongs to one of the classes of ternary semigroups; regular, inverse, orthodox and strongly regular.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, Bruck-Reilly extension of a ternary monoid is defined.
📊
Key Findings & Data:In this study, Bruck-Reilly extension of a ternary monoid is defined.
💡
Conclusion & Impact:Additionally, some results about this construction are given which belongs to one of the classes of ternary semigroups; regular, inverse, orthodox and strongly regular.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Bruck-Reilly genişlemesi · üçlü yarıgrup · regüler

Abstract

In this study, Bruck-Reilly extension of a ternary monoid is defined. Additionally, some results about this construction are given which belongs to one of the classes of ternary semigroups; regular, inverse, orthodox and strongly regular.

Özet

Bu çalışmada bir üçlü monoidin Bruck-Reilly genişlemesi tanımlanmıştır. Ayrıca; regüler, tersinir, orthodox ve strongly regüler üçlü yarıgrup sınıflarından birine ait olan bu yapı ile ilgili bazı sonuçlar verilmiştir.

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Cite This Article

Ünal, S. O. (2021). Bruck-Reilly extension of a ternary monoid. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 23 Sayı: 1, 252–258. https://doi.org/10.25092/baunfbed.850352

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References (25)

  1. Bruck, R. H., A survey of binary systems, Ergebnisse der Mathematik, Neue Folge, Vol. 20, Springer, Berlin, (1958).
  2. Reilly, N. R., Bisimple w-semigroups, Proc. Glasgow Math. Assoc., 7, 160-167, (1966).
  3. Munn, W., On simple inverse semigroups, Semigroup Forum, 1, 63-74, (1970).
  4. Asibong-Ibe, U., *-Bisimple type A w-semigroups-I, Semigroup Forum, 31, 99-117, (1985).
  5. Howie, J. M., Ruskuc, N., Constructions and presentations for monoids, Comm. in Algebra, 22, 15, 6209-6224, (1994).
  6. Karpuz, E. G., Çevik, A. S., Koppitz, J. and Cangül, İ. N., Some fixed-point results on (generalized) Bruck–Reilly ∗-extensions of monoids, Fixed Point Theory Appl., (2013).
  7. Karpuz, E. G., Automatic structure for generalized Bruck-Reilly *-extension of a monoid, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68, 1895-1908 (2019).
  8. Kocapinar,C., Karpuz, E. G., Ateş, F., Çevik,A. S., Gröbner-Shirshov bases of the generalized Bruck-Reilly _-extension, Algebra Colloquium, 19, 813-820, (2012).
  9. Kochin, B. P., The structure of inverse ideal-simple w-semigroups, Vestnik Leningrad. Univ., 23,7, 41-50, (1968).
  10. Munn, W., Regular w-semigroups, Glasgow Math. J., 9, 46-66, (1968).
  11. Oğuz, S. and Karpuz, E. G., Some semigroup classes and congruences on Bruck-Reilly and generalized Bruck-Reilly -extensions of monoids, Asian-European Journal of Mathematics, 8, 4, (2015) DOI: 10.1142/S1793557115500758.
  12. Oğuz, S., Special semigroup classes over some monoid constructions and a new example of a finitely presented monoid with a non-finitely generated group of units, Cumhuriyet University Faculty of Science Science Journal, 37, (2016)
  13. Oğuz, S. and Karpuz, E. G., Finite presentability of generalized Bruck-Reilly *-extension of groups, Asian-European Journal of Mathematics, 9,4, (2016)
  14. Piochi, B., Congruences on Bruck-Reilly extensions of monoids, Semigroup Forum, 50, 179-191, (1995).
  15. Shung,Y., Wang, L. M., *-Bisimple type A w2-semigroups as generalized Bruck-Reilly -extensions, Southeast Asian Bulletin of Math., 32, 343-361, (2008).
  16. Cayley, A., On the theory of linear transformations, Cambridge Math. J., 4, 193-209, (1845).
  17. Lehmer, D.H, A ternary analogue of abelian groups, Amer jour of Math., 599, 329-338, (1932).
  18. Los, J., On the extending of model I, Fund. Math., 42, 38-54, (1955).
  19. Sioson, F.M., Ideal theory in ternary semigroups, Math. Japonica, 10, 63-84, (1965).
  20. Santiago, M.L.: Regular ternary semigroups, Bull. Calcutta Math. Soc., 82, 67–71, (1990).
  21. Sheeja G., Sri Bala, S., Orthodox ternary semigroups, Quasigroups and Related Systems, 19, 339 – 348, (2011).
  22. Santiago, M. L. and Sri Bala,S., Ternary semigroups, Semigroup Forum, 81, 380− 388, (2010).
  23. Kellil, R., Green's relations on ternary semigroups, Semigroup Theory Appl., 6, (2013).
  24. Cliford, A. H., Preston, G. B., The algebraic theory of semigroups Volumes I and II, Mathematical Surveys, Number 7, AMS, (1964 - Vol. I), (1967 - Vol. II).
  25. Howie, J. M., Fundamentals of semigroup theory, Clarendon Press-Oxford, (1995).