Minimality and Maximality of Ordered Quasi-Ideals in Ordered Ternary Semigroups

The notion of ternary semigroups was introduced by Lehmer in 1932. Any semigroup can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup. Our aim in this paper is to develop a body of results on the minimality and maximality of ordered quasi-ideals in ordered ternary semigroups, that can be used like the more classical results on unordered structures which studied by Choosuwan and Chinram in 2012.