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

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 -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, -filters) of -regular (resp. -regular, -regular) ordered semigroups have been characterized in terms of its prime generalized -ideals (resp. -ideals, -ideals)