Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CHARACTERIZING THE MINIMALITY AND MAXIMALITY OF ORDERED LATERAL IDEALS IN ORDERED TERNARY SEMIGROUPS

  • Iampan, Aiyared (DEPARTMENT OF MATHEMATICS SCHOOL OF SCIENCE AND TECHNOLOGY NARESUAN UNIVERSITY)
  • Published : 2009.07.01
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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].

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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. 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
  3. 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
  4. D. H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math. 54 (1932), no. 2, 329–338 https://doi.org/10.2307/2370997
  5. F. M. Sioson, Ideal theory in ternary semigroups, Math. Japon. 10 (1965), 63–84

Cited by

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