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CHARACTERIZING THE MINIMALITY AND MAXIMALITY OF ORDERED LATERAL IDEALS IN ORDERED TERNARY SEMIGROUPS
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 Title & Authors
CHARACTERIZING THE MINIMALITY AND MAXIMALITY OF ORDERED LATERAL IDEALS IN ORDERED TERNARY SEMIGROUPS
Iampan, Aiyared;
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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].
 Keywords
ordered semigroup;(ordered) ternary semigroup;(0-)minimal and maximal ordered lateral ideal and lateral (0-)simple ordered ternary semigroup;
 Language
English
 Cited by
1.
On Ordered Ternary Semigroups,;;

Kyungpook mathematical journal, 2012. vol.52. 4, pp.375-381 crossref(new window)
1.
On Ordered Ternary Semigroups, Kyungpook mathematical journal, 2012, 52, 4, 375  crossref(new windwow)
 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 crossref(new window)

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 crossref(new window)

4.
D. H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math. 54 (1932), no. 2, 329–338 crossref(new window)

5.
F. M. Sioson, Ideal theory in ternary semigroups, Math. Japon. 10 (1965), 63–84