Minimal and Maximal Ordered n-ideals in Ordered n-ary Semigroups

Anusorn Simuen, Pattarawan Petchkaew, Ronnason Chinram

Abstract

The notion of ordered n-ary semigroups is a generalization of ordered semigroups and n-ary semigroups. The concepts of minimal and maximal left ideals and right ideals play an important role in semigroups and ordered semigroups. In this paper, we extend these concepts to consider in ordered n-ary semigroups. The remarkable results concerning minimal and maximal ordered n-ideals in ordered n-ary semigroups are given.