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

摘要

In this paper, as a generalization of the concepts of left filters, right filters and filters of orderedsemigroups, 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 generalizednotions 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 characterizedin terms of its prime generalized (m, 0)-ideals (resp. (0, n)-ideals, (m, n)-ideals).