Left-m-filter, Right-n-filter and (m,n)-filter on Ordered Semigroup

Abstract

In this paper, as a generalization of the concepts of left filters, right filters and filters of ordered semigroups, the concepts, for any positive integers m and n, of left-m-filters, right-n-filters and $ (m,n) $ -filters in ordered semigroups have been introduced and some properties of these generalized notions have been investigated. Finally left-m-filters (resp. right-n-filters, $ (m,n) $ -filters) of $ (m,0) $ -regular (resp. $ (0,n) $ -regular, $ (m,n) $ -regular) ordered semigroups have been characterized in terms of its prime generalized $ (m,0) $ -ideals (resp. $ (0,n) $ -ideals, $ (m,n) $ -ideals).

Keywords

• ordered semigroup
• left-m-filter
• right-n-filter
• $ (m, n) $ -filter