Journal of the
Korean Mathematical Society JKMS

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 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 and lateral ($0$-)simple ordered ternary semigroup

MSC numbers: 20N99, 06F99