Characterizations of ordered semigroups by (m,n)-filters

Inspired by the [Formula: see text]-ideals of semigroups defined by Lajos and by the filters of ordered semigroups introduced by Kehayopulu, this paper introduces [Formula: see text]-filters of ordered semigroups. Some examples are presented and some properties are investigated. Moreover, a relationship between [Formula: see text]-filters and generalized [Formula: see text]-ideals of an ordered semigroup is found. Furthermore, after applying the concept of [Formula: see text]-filters to ordered groups, it is proved that an ordered group has no proper [Formula: see text]-filters.