Bir üçlü monoidin Bruck-Reilly genişlemesi

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.

Bruck-Reilly extension of a ternary monoid

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.

___

  • [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 BruckReilly 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 BruckReilly -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).
Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi-Cover
  • ISSN: 1301-7985
  • Yayın Aralığı: Yılda 2 Sayı
  • Başlangıç: 1999
  • Yayıncı: Balıkesir Üniversitesi