On New Filters in Ordered Semigroups

Abstract

Ordered semigroups are understood through their subsets. The aim of this article is to study ordered semigroups through some new substructures. In this regard, quasi-filters and (m,n)-quasi-filters of ordered semigroups are introduced as new types of filters. Some properties of the new concepts are investigated, different examples are constructed, and the relations between quasi-filters and quasi-ideals as well as between (m,n)-quasi-filters and (m,n)-quasi-ideals are discussed.

Keywords

• ordered semigroup
• (<i>m</i>, <i>n</i>)-quasi-ideal
• quasi-filter
• (<i>m</i>, <i>n</i>)-quasi-filter
• generalized (<i>m</i>, <i>n</i>)-quasi-ideal