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CHARACTERIZING THE MINIMALITY AND MAXIMALITY OF ORDERED LATERAL IDEALS IN ORDERED TERNARY SEMIGROUPS

  • Iampan, Aiyared
  • Published : 2009.07.01

Abstract

In 1932, Lehmer [4] gave the definition of a ternary semigroup. We can see that any semigroup can be reduced to a ternary semigroup. In this paper, we give some auxiliary results which are also necessary for our considerations and characterize the relationship between the (0-)minimal and maximal ordered lateral ideals and the lateral simple and lateral 0-simple ordered ternary semigroups analogous to the characterizations of minimal and maximal left ideals in ordered semigroups considered by Cao and Xu [2].

Keywords

ordered semigroup;(ordered) ternary semigroup;(0-)minimal and maximal ordered lateral ideal and lateral (0-)simple ordered ternary semigroup

References

  1. M. Arslanov and N. Kehayopulu, A note on minimal and maximal ideals of ordered semigroups, Lobachevskii J. Math. 11 (2002), 3–6
  2. V. N. Dixit and S. Dewan, A note on quasi and bi-ideals in ternary semigroups, Internat. J. Math. Math. Sci. 18 (1995), no. 3, 501–508 https://doi.org/10.1155/S0161171295000640
  3. D. H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math. 54 (1932), no. 2, 329–338 https://doi.org/10.2307/2370997
  4. F. M. Sioson, Ideal theory in ternary semigroups, Math. Japon. 10 (1965), 63–84
  5. Y. Cao and X. Xu, On minimal and maximal left ideals in ordered semigroups, Semigroup Forum 60 (2000), no. 2, 202–207 https://doi.org/10.1007/s002339910014

Cited by

  1. On Ordered Ternary Semigroups vol.52, pp.4, 2012, https://doi.org/10.5666/KMJ.2012.52.4.375